Both UA and AA(7 mainline rt) & AS (1 rt) fly LAX-SFO. Pre-9/11, UA had service at 30 minute intervals, and at certain times every 15 minutes, mostly with the 500's, but also with other aircraft that were tag end/originators.
I think the viability of the route depends on what happens to UA. If the tulip dies, then the new US might have a good chance. Remember, AE, UX and SW fly LAX-SJC, while UX & SW fly LAX-OAK. JB flies LGB-OAK, and don't forget SW from BUR & ONT to the both OAK & SJC as well as UA/UX from BUR-SFO. To get to the SF financial center it's almost quicker and easier to fly to OAK and take the Bart.
Another consideration is where US ends up at LAX. If they stay in T1, a shuttle will be a mess, now that numbers of travelers is back to pre-9/11 levels. There are only 8 security lanes in T1, and in the morning you are lucky if you aren't in line down by T2. Of course when the club was open you could skip all that.