I've always thought a cool idea would be have a robot in the lead role of the player. Robot gets blown up? You rebuild it. Robot gets smashed? Rebuild it. Robot gets arm shot off? Slap a new one on.
Slap a better one on. One that has a chainsaw instead of a hand. etc.
Best of all, robot starts with a blank slate. You switch robot on for the first time, and he's never had any past experience with anything. He may have skills programmed in to him, but otherwise he's a void which explains the 0 EXPERIENCE level thing nicely as well.
What's even better, is that for robots, you don't have to record voice-over, you can just pump out some Hawking-esque synthvox, and you don't have anyone whining that they have to read everything. You can also completely sidestep referring to the avatar in vague terms (vault dweller, chosen one, hey you) and use whatever name the player gives themselves.
Another groovy thing would be playing around with Philip K Dick's favourite theme, of robots with human thoughts and emotions and the setting builds itself. Robots are built to serve humans, and are treated as machines. As the player character, you need to rise above human oppression, and either dominate humanity or find a way to happily co-exist. There's infinite potential for great societal themes and satire and it's very easy to rationalise advancement and skills within the framework of upgrading robotic systems, software, ressurection and repair are plausible, and there's a lot of flexibility within the setting. Robots could be anything from retro styled (Forbidden Planet, Lost in Space, The Day the Earth Stood Still) to replicants (Blade Runner, Westworld, Terminator) or something entirely different.
It's also fairly easy to rationalise various resource based facets of general RPG systems as energy. A power reserve to represent stamina, capacitors for action points, or even an induction coil or a secondary energy reserve for "mana" and various electrical impulses for "magic" depending on the setting.
Basically I can't see a lot wrong with a robot based RPG.