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.
I have been waiting for the electrician to hardwire the battery for about six months. He said he would stop by next week. Once he has done that, I will increase the maximum charge/discharge power to 1500 W (conservative, I know, but I think I don't need more to fully charge/discharge the battery on regular days).
This isn't a grid limitation but a rule about safe home installations. The limits are low for things the general public gets to plug in on their own. Those simple limits don't apply to the same battery installed by a professional. Professionals would instead follow a more complex set of rules and make some calculations, allowing for much higher currents if done in the right way.