Sure, as long as you believe you must never change the laws around housing. In that case, you can stop the whole conversation there.
On the other hand if you wanted to actually do something you could pass a federal law or constitutional amendment giving individuals the right to posses no more than one home without undue restriction. For example, construction codes simply get more and more strict across the nation each year. For the simple reason that the industry lobbies for it, as it increases their opportunity for profit. There's no actual need for this as it isn't like humanity hasn't been building homes for thousands of years.
If housing prices are rising in the area then generally (not always) there's more demand for housing than supply. Increased density generally leads to increased economic activity (more housing = more residents = more commercial activity = higher tax revenue.) Viewing the housing market in isolation is a mistake.
> But if all you're doing is making housing more financially affordable, you're going to have to deal with the fact that Peter's financial savings is Paul's lost rent-seeking, and Paul is generally a pensioner that votes.
Yes and that's the problem. Veto powers in most residential politics tend to be strong and so Paul's veto generally overrides Paul's demand.