Hehe, stop trying to bring reality into this argument
We have a concern, that LI are underpowered, and *overused* by the AI. In order to fix this you can either play with the costs/stats of the LI (won't fix it really) or change some mechanics to make LI more useful in general.
The problem with tweeking LI values, is that since the controling factor at some point is going to be supply you will never want alot of LI consuming the supply for your better troops. Ok you can raise supply with artifacts and nature mages, but that's an artifical solution and one that not every nation can easilly attain. Upkeep is seemingly secondary, but it is also a problem, especailly when you combine it with supply.
If LI and HI have the same supply and upkeep needs its obvious that unless HI is soooo grossly overpriced that you can't afford them you will eventually not use LI at all. As it stands now from what I can tell, there isn't even an early period where LI are useful, you go for HI (or MI) right off the bat, you never use LI.
Now if LI got some boost (free upkeep and supply for 10 LI for every province you control) then you'd be a fool not to use that free amount. Getting back to reality for a sec... this is what usually happened anyway! The LI were cheap to raise, and cheap to maintain, remember that the concept of supply in Dom is abstracted (or can be) to account for a variety of supplies, not just food. Any army with a significant amount of armor or better weapons required craftsmen to maintain and repair those weapons, the supply use in dom then could be higher for the HI to account for these craftsmen (or lower for the LI since they don't need them).
This should be first and foremost an issue of game balance and whats the best game mechanic though, not one of what's more realistic, how much food does a guy with plate mail need compared to a naked farmer...