It's absolutely insane. You are seriously underestimating how much time and energy you will burn on travel. I go back and forth between the east bay and Phoenix every week or so and it is minimum of 3.5 to 4 hours door to door when I fly SFO (for a flight that's about 30 minutes longer than SFO-LAX). And that's using Uber/Lyft and avoiding trafficky times of day in the bay area. With BART and LA traffic, you're looking at well over 4 hours door to door.

You're burning a huge part of your day and you have to schedule everything around the travel. That's not even talking about the stress of dealing with getting back and forth to and from and then dealing with the airports and airline nonsense.

And we haven't even discussed the particular dysfunctionality of LAX or BART (which you apparently will be relying on to cross the bay). BART frequency from SFO on the Antioch line is one train every 20-30 minutes for most of the day. And I encounter BART problems (canceled trains, mechanical issues, police activity on the platform) about a quarter of my SFO trips. (Yesterday, for example, we stopped just short of the platform at SFO and just sat there for 15 minutes because the train that was supposed to have departed already was having "mechanical difficulties.")
Definitely OAK, and depending on where in LA, possibly BUR or LGB.