I personally don't think it's "stupid", but yeah I prefer medkits-hunting between these choices. And if I may add, I think it's better if there's an animation of your character healing him/herself instead of insta-heal when you pick it up. This can be found in Fortnite, or Far Cry where the character pulls a bullet out of his arm (although that's also kinda absurd when he got shot in his chest but the bullet came out of his arm). That makes medkits more realistic.
But even so, I don't mind having the health regen mechanic, because then again games let us do things that we can't in real life. But, the game has to made it believable enough to not be absurd like you said, 5 seconds of hunkering down and you're as healthy as ever.
Maybe use healing spell in fantasy games or something like that to make it less like a lazy gimmick. That's one example I could think of.