Most generator sets will have a prime mover sized to generator output.
On farms it can be common to see tractor PTO driven generators. Some guys run these with a tractor that is much larger than needed for the generator rating.
Back in 2005 we had ice storm that took power out in large area and some out of power for week or so. I had a guy that to get some corn out of a bin to feed cattle, but this bin was not on same utility service as other parts of the farmstead and had no transfer switch on it.
He decides to directly wire the auger motor to the generator, turns breaker on the generator on to start motor and it breaks universal joint on the PTO drive shaft.
He has me out there and asks what happened there, I looked and he miswired the motor connection - somehow got incoming L1 and L2 tied to the same point so bolted fault. Had he been running more appropriate size tractor for the generator output it maybe would have killed the engine, or at least be a noticeable load on it?