I think PHL transcon service suffers due to a combination of its location between D.C. and NYC, and AA's dominance in PHL keeping other legacies small there.
Eh, I think PHL transcon service suffers mostly because Philadelphia is relatively poor for large metro areas and the finance/entertainment industries are not as important there (Scumcast being an obvious exception). Fare levels from L.A. to Philly are lower than to WAS, NYC, or MIA/FLL and broadly similar to BOS -- but BOS is a much more competitive market with five carriers operating non-stop to LAX. L.A.-Philly is a smaller market than all of those -- it even punches below L.A.-Atlanta and L.A.-Orlando though fares to MCO are about 15% lower than to PHL. Still, in a highly competitive market like LAX-MCO that's not a huge discount compared to the LAX-PHL near-monopoly. One can basically say the same about SFO-PHL except that SFO-BOS does quite a bit better than SFO-PHL and SFO-PHL is slightly larger than SFO-MCO.
Regarding LGB, I think WN could reasonably run an operation of ~25x daily flights from there (SMF, OAK/SFO/SJC, LAS, PHX, DEN, maybe HNL or OGG).
They've already announced AUS -- I have to wonder if they had some info about B6 exiting LGB or were just exerting pressure. I think they go 4-5x in the short-haul markets -- OAK, SJC, SMF, LAX, PHX, DEN -- with maybe a handful of single dailies to places like MDW, DAL, HOU, and STL. BWI would be a real dark horse. Assuming the industry recovers to near pre-Covid levels I'd guess they get to around 30 daily departures.
I don't think anyone expects them to be as important as big 4 in LA Area. But they do have an opportunity to be more relevant than they are now. I'm sure there are many network benefits to having greater presence in LAX. Maybe it will help them get more corporate contracts on these important mint transcon routes. And there is also the possibility of them of getting more of the old VX crowd.
But they have to put a real effort here. They need to have as many mint, newly configured A321Ns and A220 over here as possible. They need a product differentiator if they want to establish themselves. And they have to eventually at least service places like PHX and DEN a couple times a day.
I think that getting a minimum viable selection of destinations and schedules will be more important than product. Product is nice to have, but they're not going to get corporate contracts without a broader network from LAX. Presumably they get that, but they need to serve places like PHX, SMF, PDX, and DEN, rather than RNO and BZN.