As an side note, this is almost the same as proposing price controls for the entire real estate market, since the price of land and housing are closely linked (at least in SF).
https://en.wikipedia.org/wiki/Price_controls
Let's say we implement full controls tomorrow in SF, where all real estate appreciation is capped at, say, inflation.
As demand for housing continues to grow, you'll find that the government-mandated capped price will rapidly diverge from what the free market price is, e.g. someone is willing to pay $1mm for a house but it can only be sold for $600,000.
Since the seller is essentially being forced to take a bath, property owners will simply not sell. The market becomes extremely illiquid and everyone loses.
The key to understanding the seller's behavior, by the way, is because under price controls the market becomes extremely asymmetric. An excess of demand means that every potential seller has MANY potential buyers who are all willing to pay the asking price, so buying becomes a huge lottery. So if you own a property and you sell, there's very little chance you can change your mind later on and buy a different property, whereas in a normal market you just pay the normal transaction fees.