I think the problem is that teachers' salary is from the "school funding" budget. Here in Germany it's different per state, but in my state (at least when I was

I think the problem is that teachers' salary is from the "school funding" budget. Here in Germany it's different per state, but in my state (at least when I was in school) - ALL the teachers of ALL public schools were paid by the state directly, and according to a fixed table, it didn't matter if you worked in a rich district in the city or somewhere on the countryside (or let's say small town for a high school). So yes, of course housing prices can still be vastly different (and of course teachers who live on the countryside might have a house and the ones in the city may rent a small flat) but it wasn't a real problem that they couldn't afford housing, especially on a district basis.