Recharge Litium Power Station with RV Alternator?

[BCam]

I'm late to the party and may be missing something, but why not just run your generator while driving to charge your power station from a 120V socket? This doesn't require any wiring, additional equipment, etc. The additional fuel use would be minimal. Many of us run our generators while driving to power our A/Cs, etc. I can't see any downsides.