I personally like many of the suggestions made. War is not easy. It is downright costly. Your ability to control your regions deteriorate as your lords are off fighting. Your unit expense rises doe to repairs and replacement. A system that helps mitigate some of these effects would encourage battles.
In addition to a realm bonus I would make some of the bonus to regions specific to regions. So, if Region X has a Lord and two knights, then the region will gain productivity/loyalty/authority bonuses based on how many battles it's nobles participate in. I would also suggest that the bonus granted by Lords be a higher than the bonus provided by knights. This would allow the lord/knights of a region to maintain his region either by fighting like mad or by sitting in the region and holding court or otherwise actively managing it.
I also like the idea of finding ways to reduce the costs of war. If your men are constantly and actively collecting valuables from the battlefield they would cost less to maintain while in the field. They still die though and trips back to the capital would be a good check and balance. Reducing repair costs and payments to units would certainly make any noble with a unit want to keep the battles going. I think balancing things so that you could afford a larger unit during times of way than during times of peace would be good.
I would probably keep too much peace around. As others have noted it serves as a good reminder. I think it should be less damaging though and primarily make units more expensive to maintain at large numbers. The occasional desertion might be good way of achieving this. "Your men grow weary from the lack of battle. One has deserted in search of glory elsewhere." Now you have to replace that man and train up. I would not want to extend this desertion to militia, as they are home bodies anyway, and I would keep the desertions low enough that the realm can overcome it with only some additional expense.
