The reason I think it's this way has to do with taxes.  Here, property taxes fund the school district.  My school district's property taxes are relatively high and our school district is rated well.  Tax rate increases and bond  issues are decided by election and usually pass.  Let's say the adjacent district hasn't voted to pass those higher property taxes and  bond issues, their school would not be funded the same as ours.  Should a resident of the adjacent district be able to send their child to ours?  They aren't paying those higher property taxes.  I do know that some out-of-district kids attend our school but their parents are charged for it.

You make an interesting point about this possibly being a racial issue.  I'm not sure.  My granddaughter is a teacher at a district in a low income area.  This district is rated highly and the teacher pay is good, compared to others.  So, I am assuming the citizens there choose to fund their school well.

Please don't take this reply as the gospel.  I'm just telling you about my feeble understanding of my local area.  There may be a lot more to this than I grasp.

In the state I grew up in, schools (other than the title 1 schools, which got federal and state funding) were almost entirely funded by local real estate taxes. The state contributed almost nothing to the district I attended.  Only students who lived in the area that supported a school through taxes could attend that school.  In my current state, which provides more state funds to local school districts (although they're still mostly funded by local real estate taxes), we have some school choice - you can apply to attend an out of district school and if it has available space you will be allowed to attend. School district residents have priority, of course, and there's no busing available to out of district students. 

The school districting makes total sense, IMO, in light of how our schools are funded. 

Local taxes do pay for schools, but it can also be used as a form of "legal segregation" since drawing district lines is arbitrary. Here in Anti-Canada, school districts are divided by townships, with some rural areas having one system serving many townships. That does mean that kids living in the same county could get vastly different educations depending on county demographics. Growing up, I lived in a very suburban, affluent area of our county. Go west 10 miles and you hit farmland. I lived on the edge of the township and worked in another township. The education difference - including differences in school start date, activities offered, and even "levels" of class difficulty - was substantial. But, my parents paid twice as much in taxes as my rural counterparts, so my school had more to offer (for better or worse).

School choice has become more of a thing here, especially in the city. So long as you live in the county and have transportation, you can switch schools, so long as the school has enough capacity to accept more students. There isn't a fee unless you live out-of-county, but if you do, you'll pay annual tuition. We also have a school voucher program that allows parents to basically take their tax dollars and use it to pay for private and charter schools, which has created a BIG problem for public schools and is a politics nightmare. They've also accredited several online schools, and I believe one of those programs embezzled funds without actually producing content while having students enrolled.

Oh, and public school isn't free, either. There are annual fees that can top multiple hundreds or even thousands of dollars, especially in high school. So, even if a parent has school choice, they still have to be able to pay the school fees. Not paying them won't keep a child out of school, but it could prevent a child from getting their diploma issued. Because nothing says "let's raise kids up and out of poverty" like holding their key to more education and a better life hostage because their parents are impoverished (or suck at being parents a la the HCBM/Fs on this board).

Yep, it all has to do with property taxes and neighborhoods. Schools will assign students to that school depending on their location/address. Certain neighborhoods tend to have demographic tendencies. Ex. a Title One school might be surrounded by all low-income neighborhoods. Some schools are more diverse than others. But it totally depends on the surrounding neighborhoods and what their demographics look like. Majority of people view the lack of diversity as a problem. However, people in the high-income neighboods, that have to pay the high property taxes. And who decides the property tax amount? Local county government does the appraisals. Higher income neighborhoods tend to have the "not in my backyard" mentality. They support the idea, but don't want it to directly impact their own children. Many people who pay the high property taxes feel entitled for their child to attend a "good school", since they are paying so much. I can understand both sides. 

Education is considered a "local control" issue, so each state sets their own structure for school districts. In some states, each town/city has their own district, this is largely due to historical reasons when an individual school was set up to serve the local town and cities and towns hold very tightly to control over their schools. This perpetuates inequities in many ways, since who can live in the city / town is determined by how affordable it is. Other states set up districts by county, which is a way to theoretically ensure that resources are more evenly distributed, but there are still issues depending on the size and demographics of the county. Some states have revised their districts so they all serve the same amount of students, this is supposed to help with resource distribution, but there are still issues due to size and make-up of the district. Some states have districts that cross town and city lines, these are also for historic reasons when "unincorporated" areas were added to school districts first and then towns/cities later and the two didn't always line up. Most states have a mixed funding model that relies on some local funding (property tax) and state funding (sales tax is a common one in states without income tax). Some states used to operate under a model that was entirely based on property tax that all went to the schools in that city or town, but that led to huge disparities because real estate is worth more in some areas than others and also led to lawsuits because many state constitutions guarantee an "equal" right to education for all citizens, so most of those states now take a cut of the property taxes and redistribute them. Some states have property tax caps or other regulations that impact how money can be spent. I'm vastly oversimplifying, but school districts are a symptom of the fragmented education system in this country, which is caused primarily by it being a state, not federal, issue and that it's further viewed as a local control issue in many states. That's also why school boards exist, to add another element of local control. 

Such as Rochester NY, they have maps drawn up with racial/ethnic compostiion aka microdistricting.

In the eighties and nineties I was told that my caucasian daughter could only walk to a local school up to 4 miles away but my bi-racial son could be bused several miles away to a "magnet" school.  I thought this was highly unfair since they are brother and sister and lived in the same household.  They literally pointed to their map that had symbols for races/ethnicities and where they were allowed to go based on the demographics!

I ended up complaining about it so that both bios could go to the same school (elementary and middle school on the same lot).

And yes people pretend to live in certain "better" school districts by using a relative's address in order to gain access to that school.   

I went to middle school and high school in western PA, and districting there was very very strict. The only kids who attended a different district had either been expelled from their local, were bullied to the point of self-harm and allowed to change, or used another relatives address. It came down to tax $, fears of overcrowding in the better school districts,  and sports recruitment. Sports are HUGE in western PA and before they implemented the strict rules, HS's were recruiting like colleges, so you would get one school totally stacked in every sport. Even when I was in HS, there were cases to keep kids from playing sports that transferred schools even public to private school. I was one of them, couldn't play any sports my junior year because I switched into a private school with a good sports program. My reason for switching was my parents were moving between districts and I already had enemies in the new district that would have made my last 2 years of HS hell, I begged to go to the private school and got a job to help pay for it, but it was ruled that I changed to be in a better sports program...

I grew up in Albuquerque. School placement was based on your home address. Looking back on it now, it was kind of class structured. I lived in an upper middle class neighborhood.  This was in the 80s to mid 90s. 

Now I live in a smallish town in the South. Our schools are in a county district rather than a city one. We have 1 high school with 3200 students. It's been overcrowded for years due to the influx of military families.  You can basically choose which school your kid attends other than Collegiate which requires testing and vetting.

For a small town, the curriculum is great. They know that not everyone is college bound. OBS graduated in June with EKG certification and EMR qualification plus advanced welding education. He starts at our local community college next week, with the hopes of an AA in physical therapy. YBS is in his second year of engineering and mechanical drafting. He took welding last year and showed some decent skills but after getting flashed a couple of times he's switched to HVAC. He's talking about going to technical school after graduation so he can tie them together. 

Our schools offer waivers, so we have a lot of kids from surrounding areas coming in.