Better would just be making gains due to inflation tax-free - it makes no sense that capital gains aren't indexed to inflation. Tax the real gains, not the nominal ones.

You get a 250,000-500,000 exemption for a home you actually live in for 2 years.

Tell that to someone who lives in a perfectly ordinary, well maintained single family house in what is now an expensive part of the Bay Area that would sell for $3.5M, and whose basis is essentially zero. If they want to move to a nice condo selling for $2M, they can probably squeak by, but most of that $1.5M gain will disappear.

This is a problem for people who want to move. But, and this is mostly speculation, this is bad for everyone else too. It makes the market less liquid, which means that people are less likely to live where they want. It also reduces the incentive to build the kinds of units people want to live in. Suppose you want to build 100 nice condos. It’s harder to sell them to existing homeowners, and, in turn, those owners’ homes don’t go on the market. With fewer houses on the market, a smaller stream of buyers with lots of money can keep buying houses at unreasonable prices, and the market prices get pushed up.