Not unusual for the converter to share its 120v breaker with a receptacles' circuit. It/they only need 15a/14 wire, but of course you have to "manage" what 120v things you plug into the shared receptacles with the converter charging low batteries so it is drawing its full need.
If you ever run an inverter "whole house" (shore cord plugged into inverter) so you need to turn off the converter, it can be a problem if the those receptacles are the ones you want to stay "live" to run the television or whatever.
So it is useful in that case to have the converter on its own breaker so you can use the breaker as the converter's on/off switch. Otherwise you would need to wire in a new switch for the converter's 120v before it gets to that shared breaker.
Also, AFAIK the whole idea of 50a instead of 30a on the 120 side, was so you could run two air-conditioners. So both A/C should not be on one leg, or what's the point?