I'm not clear what point you're making about PDUs.

Re 120V outlets, while batteries don't need to supply the full peak load, they are more effective the more of it they can supply. And a home with a heat pump or baseboard heaters, electric range, EV charger, or dryer for example is going to at times significantly exceed the capacity of the 120/15 outlet. Doesn't mean the battery would be useless, just that it wouldn't be as effective at its primary purpose of load shifting as a 240V system, and therefore less economical.