Another thing to note is that you take damage rather quickly in Vanquish and don't have a lot of HP. A medkit restoring only 50% HP in this case would be pointless
That's hardly a compelling argument in favor of regenerating health. Most games with regenerating health have fragile protagonists, because at some point the developers realize that with the absence of health management, it's the only way to introduce some modicum of challenge (albeit not a very interesting kind of challenge). Adam Jensen for example instantly dies from a 3-foot fall without the Icarus landing augmentation. Vanquish doesn't have regenerating health because the player character is fragile, they made the player character fragile to justify the use of regenerating health.
The player is made fragile because you have no business walking around being able to tank bullets when you should be sliding away from bullets instead, hence why you die so fast. Especially because like I said before, Vanquish doesn't play the long-term game, and with medkits you'd be in a critical state for longer than need be as you're desperately trying to find your way back to a piece of cover which has a medkit behind it, slowing the game down as you're trying to heal yourself. There's not a whole lot health management would add to Vanquish, and more it would diminish. If you had more health, then you could bruteforce your way through more by tanking damage and playing the popamole game. Whereas with less you'll be forced back into cover more often, and if you want to
go fast without receiving critical damage you'll have to think outside the box.
Having to twiddle thumbs around health management would slow the game down, which is exactly the very opposite Vanquish is going for. It'd make things more 'tactical', but
this is not that kind of game. It's about going fast in the here and now without having to worry what happens in the future. If you want to make a better case for why health management would improve Vanquish, you should explain how it would improve
what Vanquish is going for. If the incorporation of health management would break several existing elements and would have to involve changing several key aspects of the game to the point where it can't be called the same game anymore, it isn't necessarily improved, but just changed.