Suburbs are expensive as hell for cities to govern. Population density is low, there's no commercial taxation opportunities, utilities and services have to cover more ground, and so forth. Developers love suburbs because they have a low startup cost: you buy a few acres of land, throw a few thousand bucks to a civil engineering PE to plat it, and start selling to builders. Mixed-use development requires ages of collaboration with city planners, permit denial rates are much higher, and then once you can break ground you have to invest hundreds of thousands or millions of dollars and hope you make it back with rent.

Mixed-use development requires ages of collaboration with city planners, permit denial rates are much higher, and then once you can break ground you have to invest hundreds of thousands or millions of dollars and hope you make it back with rent.- didn't know it's this way in us. Here in EU developers are happy to build as high as possible with first floor reserved for businesses to a point where cities are thinking auch a high density may affect negatively the life of the other ppl since the infra/schools nr etc aren't designed for it. And ppl are buying this stuff like hot pancakes

Then why is the amount of new housing built in EU so low, compared to US?

That's not zoning. It's bureaucracy and corruption. Basically politicians are bribed to give authorisations to specific companies. On the other hand, in Germany for example they just give fewer authorisations to protect the revenues from their investments in pension system. The other reason is just lost knowledge and huge effort needed to design new areas. New housing needs proper infra like schools, public transport and ao on, all of which should be planned, takes time and costs money. Some cities learned to deal with it, others didn't