HAHAHA! I feel like such a newbie. I never thought about giving them stimpacks.
Yeah, but like mentioned, they don't always use them. In fact for me at least, they rarely do. I have seen food disappear from their inventory as if they're eating them (sometimes I think I even hear the 'munchmunch' sound), but in order to preserve their life in a big fight, they still need manual healing from me. But I don't have much problem keeping them alive 98% of the time either, so I don't mind. I guess it's just how you play...since I'm always ranged, during a fight I try to stick close to them so it isn't far for me to activate their Wheel. But if your companion is ranged/you're melee (or the other way around), I can see how that would be a pain in the butt.
If they auto-healed themselves, then they'd be even more overpowered in some cases than I think they already are - especially in non-hardcoe mode where stimpacks are instant. imo it should be at least some work - both in healing and in having to keep a bit of an eye on them - to keep them healthy.
The thing that drives me crazy, however, is how I can't tell how much health they have without hovering my mouse over them to see their health bar. Usually my mouse is hovering over an enemy, not my companion.

I know they have their 'I need a doc" lines but sometimes they say that and their actual health hasn't been lowered by that much...they just have a crippled leg. I don't suppose there's a 'permanent companion health meter' gui mod floating around somewhere? Or is there a gui option for it already that I've missed noticing?