Regenerating health, by itself, really isn't so bad, nor is it a bad concept, by default. The problem is that the system has been inappropriately shoe-horned into so many games where a much different health system is needed(game developers decide to be lazy and just copy-paste a gimmick that worked in one top selling AAA game; go figure), or at least modify the rate of regeneration to be consistent with the requirement of maintaining challenge within the game. Honestly, I don't think there is a single health system that works universally. The best health system to implement will depend on the nature and strategies specific to the game being developed, not what wasq used in the last AAA blockbuster.
Off-Topic Rant: I am increasingly of the opinion that the game industry, as a whole, really needs to divorce itself of this AAA blockbuster mentality. It is a model of game design, development, promotion, and experience that, in my opinion, has only served to substantially increase cost(to the publisher, developer, and gamer), completely destroy creativity, and create a burden of risk that only the largest, most consolidated game development conglomerates(like EA) can actually bear. Also, given the cost and time commitments necessary to many of these AAA games, it seems increasingly more difficult for gamers to deal with more than a handful of games, either because they just can't afford them or they just don't have the time to play them. The model was fine years ago when only 1-2 such games would appear in a given year. But, now that this is the expected norm with almost every release and there being 4 or more such releases a year, the whole thing just seems to be collapsing under its own weight. I feel that the idea has just been extended beyond its regime of applicability.