I think the way to make generals matter is to make it cost something for the imperial army selection. Even small cost like 1-2 gold.
The way to make the generals more attractive is to make them more useful, not have the army auto-resolve penalize you.
The Generals odds of winning do get better as you advance their story, in my previous playthrough, Catherine's arc was completed and her odds of winning were noticeably better than anyone else, but mam, using them can get expensive. At one point in late Act 2, the fee for a single battle was like 30 gold. For that I could buy a bunch of units on the strategy map and boost my odds of winning for more than one battle.
Right now, with Karthan gone and Sybille down to 3 territories left (Farhan is the biggest remaining threat), his fee is 23 gold. Granted, his arc is done, it has taught him 2 new skills, and his chances to win are up to 9% (compared to 0%, 1% and 3% for the others), but that's still pretty expensive for a one-off.
