The problem is not the plug itself but the rating for the circuit it's connected to. If there is a 16A breaker for the circuit to protect the wiring from overload but you add 10A via a plugged in battery you're now allowing a total of 26A to flow through those same wires.

The 800W is a compromise, the wiring for a 16A circuit (typically 2.5 mm2) is able to handle 20A without a fire risk.

If you install the same battery in a fixed setup by an electrician it would be on a dedicated circuit so the only limit is the wiring of that circuit and the breaker you let them install. They would then also consider limits on the upstream wiring and things like earth fault protection.

I had separate circuits installed for my solar and future battery, using 4 mm2 wiring and 25A breakers. Only a small change to the central installation swapping the earth fault protection for one that was rated for higher currents.