Because it allows the devs to be lazy. They don't have to spend much time balancing enemy DPS, enemy awareness, enemy response and accuracy, health drops, and game mechanics that allow player skill to avoid damage. MGS had enemies with cones of vision, movement patterns, attack patterns, avoidable and dodge-able attacks. Games of this ilk allow you to beat the game without ever taking damage if you are good enough.
Now with health regen they can just make it so the enemies always know where you are (no complicated AI detection procedure needed), have perfect aim (no complicated enemy skill calculations), and shoot you the instant you reveal yourself to start doing damage to you. But it doesn't break the game because you can just hide and heal anywhere. Lazy design.
The argument is that it keeps the player engaged in the battle by keeping them pushing forward rather than looking for health pickups. In practice, it means lazy levels, with lazy simplistic enemy AI, with lazy design that requires health regen because it is impossible to not take damage.