And even many affordable neighborhoods of 1960's-looking-suburbs and such, have lots of dental offices / daycare centers / insurance offices / chiropractors / photography studios / private tutors / etc in them. Most people never notice, because they look like any other random ranch house. But they exist, and are permitted by zoning.
Historically, some places in the US have family-housing-only zoning laws, not to enforce a "strict separation", but to protect housing affordability or protect public transportation. If you could put 'anything' on that land, it would cost more, preventing people from being able to afford to live there. And if you could put 'anything' there, you might build a superstore or a theme park or similar (which would block other residential residents from using the public transportation network)
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Berlin has strong renter protections, rent control (freeze + cap), more widespread alternative forms of public transit, and substantial public housing. So the threat of private equity breaking the whole town is a little bit less pressing. The vast majority of America has nothing even remotely close to that. Zoning protections like these are basically the only thing preventing housing prices and transportation availability from being even worse in the US.
Unfortunately, American city planners have a lot of bad ideas of what a city should look like. For some reason, stadiums are unreasonably popular ( http://www.hatrack.com/cgi-bin/print_friendly.cgi?page=/osc/... ).
Likewise, if your city has set you up with some amenity like parking, and you plan your property purchase around it, and they take it away to give to someone else, it's quite reasonable to get mad — even if the use of that amenity was not specifically deeded to you as private property. There may be other concerns in a city to which they must yield, but it is hardly as if they are entitled freeloaders.
> it was developers and city councils who caused this mess in the first place.
I never understood why the US and some other countries have such a strict separation between normal business/work areas and many EU cities do not have such a strict separation and it just works very well.
Sure some industry which causes a lot of noise or other pollution is not allowed interleaved with housing and industries which need a lot of space tend to be outside of the city because of land cost.
But everything else can nicely interleave.
For example Berlin it's not uncommon to have small shops on the ground floor, some offices or doctors on the first floor and apartments above that. While many new buildings sadly don't have this anymore they still interleave shopping males, doctor houses and offices with apartment blocks.