You seem to be guilty of Fish Tank Thinking here yourself.
Housing costs are not divorced from the laws of supply and demand. Raising wages creates increased demand for housing, but you still need the supply! Raising wages without increasing housing supply will just make housing more expensive.
Exactly! This video goes into this phenomenon more in-depth: https://www.youtube.com/watch?v=N_GLfxaYTYI&t=2s
This has actually been a known issue for over a century with Winston Churchill even commenting on it.