In most places where property value growth is fast, tax relief does not keep up. And it can become a significant part of your home's upkeep, especially if you own it and have been there for some time. Rapid growth in value disproportional effects residents on fixed incomes. This is not a problem unique to San Fransisco, but to all "boom towns", large and small.
Additionally, services you once were able to afford such as parking, grocery stores, restaurants, etc. become expensive quickly. Think having your bodega replaced by a Whole Foods.
https://en.wikipedia.org/wiki/California_Proposition_13_(197...
Still, it's a good policy and I wish my state would pursue it. The oil boom priced many people out of their homes.
http://www.slate.com/blogs/moneybox/2016/09/22/california_s_...
There are plenty more.