This. Winning territory (and thus increasing the faction leader's influence) is of course the best way to get loyalty up. A short term fix for low loyalty (but otherwise excellent) generals is to place them in the King's stack for a while.
I wouldn't worry too much about low acumen generals, just don't make them governors. I have a house rule on appointing governors, only the "sirs" can get tabbed for the position. This makes it a little more difficult, since the brightest spark tends to be some scrub leading a spearmen unit, whereas most of the knight commanders can barely count to 2.I usually end up picking the leader of a sword or axe unit for the job.
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