This summer will be my twentieth year of teardropping. All my teardrops have had simple 12 volt systems with nothing wired for 120 volts. I keep a small inverter in the tongue box, but it's been a long time since we've used it. Maybe a decade.
All batteries have a lifespan. When a power station fails, you won't be able to replace it. You'll have to buy a new one. And of course they ain't cheap.
A much cheaper alternative is to buy a Weize 50 amp LiPo ($200 or less), a NOCO charger for it, and forgo the 120 volts. Unless there's something you feel you can't camp without that needs AC.
Plan a solar system into your build and forget the charging issue.

Easy-peasy.
Tony