To trade a rare talent like that just so you can be in search of the next superstar seems foolish. You sign him and try to build around him.
It'll take a sell job to keep Ohtani. The Angels are a mess. They essentially built their team this year much like the Red Sox did, with the expectation that they'd be competitive for a wild card. When you look at the two teams in 2022 they are doppelgangers.
They added Hill and Wacha-esque reclamation projects in their rotation (Syndergaard, Lorenzen) coupled with younger arms leveling up (Griffin Canning, Reid Detmers). Established hitters (Trout, Ohtani, Rendon) with role players (Fletcher, Stassi) and younger SSS bats hopefully leveling up (Jared Walsh). Some rookies or rookie-adjacent players that would make a splash (Jo Adell, Brandon Marsh, Taylor Ward).
Then they had a scourge of injuries, and several underperforming players that shortened instead of lengthened their lineup. They had a white-hot streak of great baseball for a month, then looked like the Upside Down, weathering a terrible losing streak and playing Sox-level baseball in July too. They fired Joe Maddon and Phil "old school redass" Nevin is not the long term solution; as a manager he makes a great third base coach and you hope they find better after 2022 (at least you pray they do you are an Angels fan).
There is not much to build around Ohtani at the moment; their pitching is fungible outside of Detmers and Canning (if he comes back solid from injury). Their bullpen is Costco Chex Mix outside of their closer (who should be traded for value). Taylor Ward was a surprise to post the numbers he has but has always shown promise. Brandon Marsh leaned into bad contact rates and makes Jackie Bradley Jr. look like Ted Williams. And as underwhelming as Duran has been for the Sox, Jo Adell has been abysmal both at the plate and in the field.
There's so much churn for LAA to be middle-road enough to vie for a wild card spot in 2023, and they'll have to fill a lot of the same holes that were leaking next year as they tried to do this year. So one more year of Shohei doesn't look like it'll be the difference maker. With no manager, no continuity in the majors, and the same GM, I wouldn't be surprised if they try to deal Ohtani since you'd essentially be trading for two players so the contract to keep him can't use standard position player or pitcher megadeal comps.