In theory, this could encourage people with larger houses than they need (eg empty nesters) to downsize, which could have an observable impact on shortages.
Obviously more supply is an important part of this too though.
If you assume there is some population whose house size is mismatched to what they want (in particular, the house is too large), lowering the transaction costs could encourage more people to move, which would mean that more people end up with an appropriately-sized house.
Federal law needs to reign in local municipality NIMBYs. Let people build ADUs and second homes on their land without insane code requirements.