Remember though the house are old there. 60 Amp services, small everything, some house don’t have grounded electrical outlets, so be prepared for that.

Heat/cooling loads are minimal in San Diego. Nothing wrong with 60-amp service. If they used cable with a ground lead built in (typically anything built post-1940), you can install grounded outlets and ground them to the boxes. Check for presence of good ground using a test lamp.

Outlets are cheap and an entire house can be done in a day or two no sweat. Other alternative (if no ground is present and it’s legal in CA) is to go with 3-prong GFCI outlets labelled “no equipment ground.” If there’s current returning through a short vs through the neutral, the outlet will trip off.

I’d be more worried about the presence of aluminium wiring or poor quality breakers (e.g. Federal Pacific) than the two points that you mentioned. I also grew up in a 1950s house with mostly 2-prong outlets. No one died or got bit over a few decades.

Previous house still had some knob-and-tube wiring (Google it).