This.
I used to like intricate rules for everything until I realized that they mostly just serve to make the game more complicated. If you have a GM and players who are committed to making the game fun and semi-sensible you don't need anatomically correct hit zone rules; you just estimate what effect the given hit could have and move on. If you do decide you need more complex rules you can still introduce them as neccessary.
An enlightenment in this regard was moving from Shadowrun 3E with its utterly complex combat system to Exalted 2E where the combat rules are so simple and flexible that they're also used for army-scale combat and social arguments with only minor tweaks. Are they precise? No, even with their per-second timing. Are they realistic? Hell, no. In fact, they go out of their way to reward improbable but cool maneuvers. Then again we're talking about a game with characters who can leap over mountains and punch people so hard they stop existing entirely.
(I do like, however, how Exalted does model injured characters being in worse shape. It does so by dividing the health levels (hit points) into groups with associated penalties to all rolls. Easy as pie and still a big step up from being in perfect shape at 1 HP.)
In fact, an even bigger enlightenment was playing (d6) BESM where there is only one kind of die roll ever and characters have about half a dozen stats in total. And it still works very well for what it does as long as you are aware it doesn't even try to be detailed. It's fairly well suited for quick fire-and-forget one-shot rounds.
On the other hand my group's role playing style is 95% character interaction with combat taking the back seat, usually being reserved for "boss" fights. Someone who wants to play a wargame with some character interaction added in is going to have entirely different preferences as a stay-out-of-the-players'-way approach won't do them any good. In their case something like the very first first-edition D&D might work: Take a wargame and put some social rules on top.