I am sure the OP will do a few other leisure trips other than what he will be flying for work, so UA has more destinations than AA/DL. Plus with SFO only an hour away you can literally go anywhere in the World.
Both AA and DL have very good network connectivity out of LAX (for all three of AA/DL/UA, LAX has a number of routes that don't involve hubs). I don't really think this is as clearcut as you make it. Basically, if you're at LAX, you're pretty free to choose one alliance and you will almost certainly have a lot of nonstop service (which is true of all the cities the OP mentioned), and at worst, one-stop service.
Also their J product stinks
It's not fully-flat, true (neither is DL's to NRT, they use the old NW planes). Some people don't like UA's though (they do seem to pack 'em in tight on the 777s, and not all UA's planes are converted yet, which means a non-zero chance of a recliner that's an older product to AA's 777 and DL's A330s).
However, if the employer is paying for J/C on longhaul... they have the option to use eVIPS/SWUs for
F, or to use a partner like NH/OZ/JL/KE. Plus there are bonuses and so on.
So really, based on his flying, the only advantage of joining AA/DL is LAX-SEA, but on other routes UA is either the same [LAX-SFO] or better.
Not entirely true. JFK-LAX is not eligible for free upgrades on UA, but would be on DL at any status level (even AS MVPG), and would be on AA at EXP.
Again, I think is a case where travel patterns and the expected status level are important to know. It's all about tradeoffs. UA might be right, AA might be right, DL might be right. The devil's in the details.