One way to analyze it is if you permanently raise the capital gains tax on houses, will that raise or lower house prices. You would think it would be the opposite direction of permanently lowering capital gains. Short term changes may be different.
Capital gains on houses is not a static percentage. If you sell a house in less than 2 years, the CG tax is high. If you do not live in the house, it is different than if you do. Many people think of their house as an “investment” so reducing or eliminating capital gains incents those at or near retirement to “cash out”. There are those that hold onto the house until they die, simply so they can pass generational wealth to their offspring. When you inherit a house, the basis of CG resets to the value of when you got it. Elimination of CG would cause a pretty dramatic reset of the housing market, because now people could sell, keep the money and pass the remained to their children. Within a year or two, this would significantly reduce housing costs because there would be a glut on the market. In addition, it would reignite the flipping market, because those old houses are usually in bad condition, and margins are actually tight on flips now, so more people would get back into doing that as a business. This would improve the job market, especially in the trades, which are generally good paying jobs.