You tax all the rent they earn due to holding the land [0], since all the reasons rent is high in SF are not due to contributions by the landowner (ie. the community put in effort to make SF desirable, yet the landowner gets all that value).
Singapore owns all the land, and then they lease it out at 99-year terms. So an individual can own property for their whole lifetime (and then a little bit more, perhaps to pass onto their children), but the can't pass it forever.
The problem they recognized was if they had indefinite landownership, and they could pass it onto their descendants, given that they're a small island nation, within a few years, all the land would be owned.
After that, future generations would have no more land to buy, and those who are lucky enough to be born to landed family would be able to charge rent those who didn't have the privilege to be born to a family with property.
Some would, yes. But the land value would be high enough that most people trying to enter the market wouldn't be able to afford the costs of buying property. Under this approach, the government can sell property at a subsidized rate to new buyers once it reverts back to them.
I think the government also wants to allow property owners to be able to profit somewhat from the growth of the value of their property, since 80% of the population owns property in Singapore.
Now, I agree that these 2 goals are in conflict, and tax policy would be the better fix. But I guess their approach does at least fix the problem somewhat.
@neilparikh's comment was not what I was referring to.
Singapore has government substantiated condos that are quite good. You have to be a citizen to get the benefits, but if you can benefit from it, someone working min wage can buy a decent place to live.
See https://en.wikipedia.org/wiki/Land_value_tax and https://en.wikipedia.org/wiki/Georgism
[0] - But let them keep all the rent from the building, since they built it with their own capital and labour.