I have seen this before and it may work for you, but I don't want the pc's to be special because they were born with the mutant gene to level up. The whole 'you are all destined to be heroes' thing isn't my bag. I want them to feel they earned it through actions, not birthright.
If you don't want a 'Big Damn Heroes' feel I definitely wouldn't recommend 5e. Classic D&D is probably best since Ftr-1s are functionally identical to 1 hd monsters and most of the other classes start even weaker. Obviously 4e is anathema to this 'you're nothing special' approach. I think it also works poorly in 3e/PF, it can be done but assuming 3e/PF NPCs can earn XP like PCs often results in worlds where the average experienced person is 6th-8th level and 1st level PCs are barely fit to clean the toilets.
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