Prices should increase in the case of increased demand. Prices must increase in that case if you want the supply to increase, which is the only way to actually meet demand.

It's how the market works ffs.

Not in isolation. But if building restrictions and zoning restrictions were lifted, and supply could meet demand, then rent control wouldn't be necessary, because the landlord wouldn't be able to get away with doubling rent.

If that's what demand has done to pricing then yes. Where are rents increasing 100% per year?