If we posit that there are people who would like to live in high-density neighborhoods and others who would like to live in lower-density areas (which seems like a reasonable assumption and matches my lifetime observations), encouraging high-density buildings to be near each other seems to serve both groups better than to have the outcome appear to be the result of randomness.
"Would like to" is doing a whole lot of heavy lifting here. I'd argue that a large fraction of people live not where they "would like to," but where they can afford.
There are people on this very page who could well afford to live in a high or low density area and are arguing the benefits they experience and their preference for high-density.
Building more housing units would lower the price of housing units. The question is, within that, how should we approach it. I don’t think plopping randomly placed high-density buildings into low-density neighborhoods is optimal compared to planned development.
When cities ban apartments from entire neighbourhoods, they're banning people from living there. It ensures only the very wealthy can. This means people have to go somewhere else. This could mean longer commutes for the poor and worse living conditions.
There's nothing stopping someone who wants to have a SFH from buying a lot and building a SFH. The problem is when cities impose housing bans that limit people's ability to live in these communities.
