Stuff with motors are, like air con and refrigerators. Those are better left on AC.

No. Trend is they are all showing up with frequency drives. Of which those inverters are rectifying to DC before making their own AC.
Efficiency gains are massive, hence why they are doing it.

You lose very little by rectifying AC

You lose a lot actually in all the small cheap rectifiers that are in every device in the house.

Where a single purpose designed FET rectifier that is built for efficiency at the breaker would be drastically better.