> Fewer sellers means buyers compete for a smaller pool of available homes, driving up prices
Uh? This is just moving the tokens around. Those sellers are still going to live somewhere, so they're either going to buy again or enter the rental market. So the "pool of available homes" is not improved by this maneuver, like, at all. At best the buyer and seller for a given transaction end up just trading places and renting-vs-owning availability wobbles transiently by a minor amount.
There is another tried and true method for increasing the pool of available homes though. It's called building more homes.