Oh - the problem with quicksaving is that developers can (and have) made really poorly balanced levels and just leaned on the fact that players will cheese through it. With regenerating health, developers can precisely design combat encounters to the flow and difficulty they want.
Hell I was playing Half-Life 2 not too long ago, virtually every large encounter ended with a huge stash of health packs around the corner. Same basic idea, worse implementation (since you need a pause in the action to replenish).
There's definitely a wrong way to do it (Resistance - terrible checkpointing and hybrid health system that is the worst of everything), but Halo got it right.
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