There are a lot of circuits in the US that power multiple duplex outlets around a room. You could plug in a solar panel into one outlet and a load into another and they would be connected by a length of Romex in the walls.

Generally that's fine and I agree, but one edge case that people overlook that I think is worth mentioning (and maybe what gp heard about and is trying to articulate) is that having an inverter or generator on the same circuit as a big energy consumer means that the breaker wouldn't see the total energy being used by the consumer, and so it might not trip even if the consumer pulls too much wattage. That's the main reason I know of why power sources should be on their own breaker - so it doesn't hide power from the breaker but forces it to go out the generator circuit breaker and back in the consumer breaker so it can be protected properly.