That’s largely correct but misses the point that the battery+pv system is legally only allowed to feed in 800W [1]. On our circuits you can draw ~3.5kW without tripping the breaker. This brings you to 4.3kW max load, which - as far as I understand - is still what all the circuitry must be rated for anyways.
The downside is that we have three phase power supply anywhere halfway recent. And that only gives you a single phase. In _most_ cases that’s fine, because you get a net-sum of all three phases at the meter, but technically you are only drawing/supplementing one out of three phases. In practice this likely doesn’t matter since different house put theirs on different phases and it all washes out.
[1] the DC side can have up to 2kW of panels. But that’s not visible to the grid
The downside is that we have three phase power supply anywhere halfway recent. And that only gives you a single phase. In _most_ cases that’s fine, because you get a net-sum of all three phases at the meter, but technically you are only drawing/supplementing one out of three phases. In practice this likely doesn’t matter since different house put theirs on different phases and it all washes out.
[1] the DC side can have up to 2kW of panels. But that’s not visible to the grid