Current is current.
A generator generates current, not KVA or KW or volts.
When I was a student engineer, my chief engineer explained it to me this way: if your generator is rated to generate 100 Amps of current, that it is it, no more.
If the load is unbalanced so that the phase currents are different, then no phase current may exceed rated current, say 100 A. Otherwise that stator phase will overheat as the excess current will result in excess heat. This is not engineering, this is arithmetic. So the KVA capability of the generator is reduced.
Does the generator care if there is zero sequence current (ie current in the neutral, assuming the generator is star connected)? In simple terms, no, current is current, but the phase current limit must not be exceeded, so permanent zero sequence current reduces the KVA capability of the generator.