That depends on if you're a health-is-meat or health-is-moxie person. Meat should be pretty easy to track. Not so with moxie.
I mean, given the ways you damage enemy health and heal your own health it's pretty clearly primarily "meat points" in a TES context. There might be some "moxie" in there, but not a whole lot.
Further, whichever it is, you'd have some idea how hard you got hit, and playing Oblivion, that's actually extremely hard to assess.
Modern games tend to have significant "hit indicators", which, when you get hit harder, go off harder - like your character makes a much louder or more significant pain noise, your screen flashes red more, maybe your character staggers, or when your close to death, the colour starts to fade, or the screen edges darken, or the like. As such, an actual bar might not matter much, but it does here.
Also characters in this universe clearly know how much mana they have and how fast it is coming back, again impossible to tell that due to a complete lack of indicators, because this game was designed in 2002, and assumed you'd just look at the bars!
I don't personally find it immersive because of the lack of indicators and high clunk factor. Games can do what you describe in an immersive way, and a mod could probably do it too, but the base game doesn't.
