Do you suppose that if we had enough oil we could just build enough desal plants and fill it up again?

In a word...yes.

I'm not saying it would be desirable, mind.

In a word...yes.

Do the math Leanan you might have some surprises.
In other words, though your statement "Given enough energy, we can solve just about any problem" holds in principle, there are HUGE AMOUNTS of "energy equivalent" consumption in many, many natural ressources we squander mindlessly.

Given unlimited (non-carbon emitting) energy, we could just build decarbonation plants for the air. Bury all that CO2, or shoot it into space.
Or leave this planet, and find others to exploit...