Yes, if demand is higher than supply, price goes up.

The problem is that demand for housing will ALWAYS exceed supply, not matter what. Even if everyone had a home, people would want bigger homes. Even if everyone had a detached home, people would want better views. Even if everyone had a detached home with a view, people would want a vacation home.

The demand for housing is effectively infinite. Unfortunately, the supply is constrained by reality. Even if we wanted to build five times as many units across the country, we couldn't. There aren't enough construction workers and there isn't enough material available.

You're suggesting that 2% of the market coming back available would help, and you're not wrong, it would help, it just would not move prices in any meaningful way for the people currently being pushed out of the market. We are building around that many units new each year, and prices have been going up 10-20% per year anyways.

Meaningful change means prices going DOWN relative to wages. That's not going to happen until land prices go down, and land prices won't go down until the government changes how we tax property so that regular homeowners stop making money off doing nothing but having got there first.