The problem is that for every unit that is built.. then the new dwellers then become in support of rent control. Even worse for each developer that is able to build, right after building the development they then start supporting rent control to prevent their prices from falling.

Basically everyone who joins the club essentially tries their hardest to shut the door once they get in.

Not necessarily. Keep in mind, property/land-owners own, as you mentioned, the land beneath their house. That land might be worth far more if it were rezoned for multi unit dwellings.

Property owners in SF are often opposed to new construction, but I don't think that they are motivated by the desire to maximize the dollar value of their real estate assets. They're happy with where they live, they often bought long ago so their costs and taxes are low, and they just don't want change, especially in medium density neighborhoods that have been stable for 75+ years. Their opposition to rezoning probably goes against their economic interests measured purely in dollar signs.

People in rent controlled apartments have a similar motivation. Their costs are very low, they don't want the disruption of new construction, and they are often concerned that there wouldn't be a place in the new construction for them. Why take that risk? The difference is that people in rent controlled units are more vulnerable than property owners. If they do find themselves out of a rent controlled apartment and on the general market, competing for the few new units that become available, they'll be displaced.

Grandma doesn't want to fight new construction because she wants to "protect her investment". If she actually wanted to maximize the value of her property she would take out a home equity loan, demolish her house, build an apartment in its place and rent it out (and maybe live on the ground floor). She just doesn't want the neighbors to be able to do that and "ruin the character" of her neighborhood.