I use -green_generals too. Generals stats remain mostly the same after a death. They just lose a star and certain types of vice/virtue are lost, e.g. valour boosting ones. I think acumen related virtues are still kept (as if the general had taught his protege everything he knows!) so your high acumen governors will always keep their high acumen, unless they are killed in battle or by an assassin of course!

It basically stops you (and the AI) getting 9-star generals too easily. And also, if one of your units gets a nice valour boosting virtue, you need to make the most of that unit before the general pops his clogs and it goes back to being a regular unit!