By "cap" I mean set a maximum level of hit points a character can acquire, let's say 20 hit points.

I realize D&D is intended to be heroic fantasy, and there are other RPG systems which are more realistic than D&D about hit points, combat injuries, etc.

But for argument's sake, if I want to stick with D&D but limit hit points, is it a simple tweak I can make as a DM or will I have to make adjustments throughout the rules and not be worth the effort?

My goal is to make the game a bit more realistic. In my opinion, the suspension of disbelief and tension that make low-level D&D fun starts to evaporate when players become nearly invincible and can take on armies & dragons single-handedly, blow off law enforcement, fall from great heights w/out dying, etc. all because they can absorb an inhuman amount of punishment. For example, I’d like high level fighters to resemble Aragorn from LOTR, who can square off against a dozen Orcs relying on his superior swordsmanship, rather than the godlike Thor who barely works up a sweat smiting frost giants.

Edit: As a corollary - should characters be compensated in other ways as they advance levels to maintain balance for high level game play?