IMO, unwillingness to live farther out on that large fraction of land that isn't the city is a bigger issue.
In a neighborhood like mine (75% SFR, 25% MFR free-standing homes in West Cambridge), you can bet that I'll object to zoning changes that would allow "just building up". I don't need the noise, traffic, additional pressures on the school system, nor do I want to live in a mid-rise and high-rise district. If I did, I'd have bought in one...
There should be other options than building in your backyard. Find underused places and build up there. The biggest problem is what to build and how: it's amazingly easy to screw this one up (too sparse? too dense? too high? too low?)
You can't simply conclude it's one xor the other.