It is literally what makes “good” school districts “good”, the household incomes of the student population. And moving to a suburban place filters that nicely. Same reason why residents will often times oppose apartment developments, since they allow lower income residents to move into the district.
But as you note, that movement petered out and more and more money came in and now those same neighborhoods are inaccessible to the same kind of people that first gentrified them.
Except that, as many predicted as gentrification became rampant, it's not really sustainable to drive all the service workers and their families out of the city center, and so now they just live on the streets outside of the cronut shops and gastropubs.
So if you give it another 10 or 20 years though, you can expect another urban flight to manifest and balance things out a little more again.
"Move to the city" (or any other already-walkable place) is part of the problem, not the solution. For one thing, people won't do it en masse. Even if they did, those too-few places would become even less affordable, plus their power/water/waste infrastructure would get strained beyond breaking. It's a very privileged and selfish position to take. Instead, we need to make more such places, reconfiguring and repurposing buildings and other infrastructure where they are and where the people are. And that takes voting power. Don't tell people to throw that away.
Infrastructure gets upgraded when the tax base arrives to justify it. Yes, you are right, "we need to make more such places", and the low-density neighborhoods closest to the city center are the most efficient places to do that.
It is a genuine tragedy that so much sprawl has been built over the last 60-70 years. Much of that construction can never afford its own maintenance without subsidy from the city centers. To make this sustainable, we must densify and contract.
Cities absorbing their near suburbs (as Detroit did long ago except for Hamtramck and Highland Park) and using weight of numbers to force change would possibly allow for greater density and more walkable areas in those places, but nowadays no current suburb would allow that to happen (because of property values, school funding, etc.) so it's a pipe dream. Transit would not be affected, since that's usually regional anyway. Again, the only way to affect how suburbs are built is to vote there. Running away helps the individual, but doesn't help society, and I'm sorry that people would rather not hear that about themselves but it's the truth here in reality.
I can't speak to Detroit, but here in Seattle, I just don't believe that's true. For example, look at Greenwood - close to the dense part of the city, it has a classic grid layout and there's already a good commercial core. Great bones, ready to pop, it just needs a zoning change and some transit investment:
https://www.google.com/maps/place/Greenwood,+Seattle,+WA/@47...
Madison Valley, where I used to live, is currently going through that transition, and may in another 10-20 years become properly urban:
https://www.google.com/maps/place/Madison+Valley,+Seattle,+W...
Compare this to a neighborhood in the suburbs, built in the sprawl era - for example East Hill, in Kent. What can be done with a place like this, full of wide roads, big box stores with vast parking lots, and meandery low-density cul-de-sac blocks which don't connect to each other?
https://www.google.com/maps/place/East+Hill,+Kent,+WA+98031/...
Move to a place like that and vote all you like, the whole structure of the place has been built around cars in a way which will be very difficult to fix. Lest you accuse me of cherry-picking a particularly obnoxious example, here's Totem Lake, equally hopeless:
https://www.google.com/maps/place/Totem+Lake,+Kirkland,+WA/@...
If Seattle relaxed its zoning and let urban development happen throughout, we could fit an enormous share of the region's population growth into the city limits. This would create a virtuous cycle where investment grows, rapid transit development becomes increasingly economical, the economy diversifies, and services improve. That can't be done in a remote suburb, because urban value is a function of proximity to resources.
> Again, the only way to affect how suburbs are built is to vote there.
Why do any more suburbs need to be built at all? Fix the cities and there will be plenty of space.
Pure wishful thinking. Is there any empirical reason to believe this would be more true with everyone living in a couple of dozen large cities (as if that can even happen - see later) instead of in a greater number of more self-sufficient smaller cities and towns within a region? It's not like every company even in your own metropolitan area wants to be in "Seattle proper" is it? I used to work at a large one that basically moved out and they're not the only one. Investors didn't seem to mind one bit.
> Why do any more suburbs need to be built at all
I never said that they should. They need to be rebuilt, not built anew. More precisely, they need to be reconfigured to avoid the waste and ecological damage of tearing down one place and then building somewhere else.
> Fix the cities and there will be plenty of space.
Fix the suburbs and you'll have plenty of space too. Consolidation can happen as easily in each town as in the central city, and without some of the downsides - increased prices and decreasing affordability (already a major problem in Seattle), power distribution, waste disposal, what traffic still (and necessarily) remains, etc. I've been to Seattle. Consolidating most of the region's population into Seattle city limits would not be a utopia; it would be a nightmare even from a new-urbanist perspective. Ditto for the many other cities I've been to. A certain level of geographic expansion is inevitable, but not all such expansion is sprawl.
More importantly, restructuring suburbs in place is the only way this can happen. People just won't move to the cities en masse. The current milieu of property values, school funding, etc. won't allow it. Changing those realities would be even harder than adopting a strong towns[1] or missing middle[2] approach in the places where people are and will remain. And that requires people voting where they are instead of running away.