Even with that structure, you could use a stimpak approach towards healing above UNC. If you want immersion, it can be based on nano-technology and not a "potion". Or a cocktail of super-coaglating agents. Immersion isn't either to do a quick battle, retreat around the corner to heal, move to the next room. Fighting isn't silent by a long shot, and retreating out of the building/cave/town 50 feet isn't going to get you healed any quicker (or any "more real" - whatever that means).
Personally, I'm on the fence. I like the idea of making hard choices, but not to the point where it's frustrating. I think a balance can be struck between the two models. I agree that using stimpaks or healing agents or whatever with impunity breaks not only immersion but also the spirit, I think. If stimpaks, healing agents, or whatever are employed, there should be a consequence - minimally a cool down period (to use a common term), where you can't use another one because of some dire consequence (stimpaks, for example, would contain adrenaline - take one too many, die of a heart attack; super-coaglating agents would potentially create thicker blood, making it harder to pump, die of a heart attack; take too many nanorobot injectors, body goes into shock). Long term use for stimpaks, for example, being the most common could easily be addiction. The "cool down" periods could vary based on what they're based on. You could use stimpaks more frequently, but they obviously heal for a lot less - making them only marginally effective. Super-coaglating agents would have a much longer time-between-use factor, but stop bleeding wounds and gives some extra health. Obviously more rare/expensive than stimpaks. Nano-tech? Well, lets say they give a nice perk of being able to slowly repair wounds over time (not an instant-get-your-health-back-ticket) but your body needs more time to process them out.
It can be a balanced approach. You can decide if you want them as an inventory item that gives a perk or if they're a one use item, or if they're crafted items (I can only imagine that stimpaks would be the only ones to be manufactured in any kind of quantity).