But, in rpgs at least, like in DA, your health only regens after battle. So even if you're in the middle of the battle, it's not going to recharge fast enough. It doesn't take away any strategic element.
In games like FF13, Valkyrie Profile 2 and Breath of Fire: Dragon Quarter, your health is regenerated from battle to battle and yet people still claim Dragon Quarter to be OMG SO HARD.
In many strategy games, your health is renewed from battle to battle, and yet these games remain challenging.
In multiplayer shooters, you have regen health and it doesn't make the games any less challenging.
It wholly depends, just like any other piece of game design. Just because a game has regen health doesn't mean it lacks a strategic element in its gameplay. If anything, especially when it comes to rpgs, regenerated and renewed health means each battle continues to be its own scenario and situation, because the developers don't have to dumb down enemies to pander to the player's need for health. This makes each and every battle a unique situation.