"I am not saying we shouldn't consider each area as important I just don't think we should structure policy so tiny areas are incentivized to fight each other and the loser is where everything "bad" gets built."
I'm not disagreeing with the result. What is the solution to the factions not fighting? I haven't heard one so far, so I'm disagreeing with your stated cause of it.
"My point is that we should be more permissive with where we build affordable housing, including and especially in more exclusive areas."
That's not a solution because there's no path to achieving it and ignores the established legal processes, such as appeals, that society has decided are fair. As you've pointed out, the exclusive areas fight it. My solution isn't worth going over in detail again, but has been raised in similar discussions on here. Basically, these problems are the result of population distribution. Creating incentives to repopulate and employ shrinking cities will provide the best overall results through economic reinvigoration of places like the rust belt, take advantage of vacant housing, and have less barriers to development of new housing.
"It totally matters because if it is the result of policy then it is something we can change."
It wasn't posed as a policy issue. It was posed as an architectural vs stability issue. Stuff like not dealing with bad neighbors or landlords can't be cured with policy anyways. Many utilities charge a connection cost per building, where you have an apartment building paying lower per resident fees than a home. And higher density often requires larger infrastructure, so it's not just cost per stretch.
"Zoning policy in general increases the supply of single family homes relative to multi family homes, decreasing their cost."
Maybe that's happened in your area, but not around here. Most of the townships around here permit higher density housing in many areas, but it's rarely built. The predominate thing bring built is single family. The zoning does nothing for the cost - the cost of a townhome is significantly cheaper than a single family home. The mortgage guarantee applies to mortgages on other residential property types as well. The tax break when selling also applies to other residential properties like condos and townhouses. I have friends and family who live in condos and townhouse- loans were not difficult to get at all. There's no merit here to support that SFHs are favored over higher density ownership.
"they still put their thumb on the scales in favor of home owners at the expense of renters who are much more likely to live in multi-family housing."
I'm not sure what you mean here. Many areas even have rent control and rent assistance. I don't see anything being done to benefit home owners at the expense of renters.