Your scenario is simply describing a massive under-supply problem, and mis-attributing causality for price increases.

If the older buildings are able to raise prices 20% with no increase in vacancies after the new build, the new build not coming in would mean those older buildings rent would be bid up more than 20%.

The people moving in who could have afforded the 30% more expensive luxury units will just have to pick from the older units and outbid lower income people for spots in this low supply, growing city (under no other scenario could you crank up rent on aging stock 20% without losing to competing landlords).