I'm going to jump in here then leave this thread as well, because it is going in a direction that doesn't interest me. However, I few points before I go.
If you are talking about what can't be done, then you are talking about a specific ruleset (or at least the baggage of one). Unless you believe it is impossible to make rules that accommodate those characters and ones that are more powerful too.
And this is why I am responding to this thread one more time. This was not the premise of the thread. I am not the OP, but I am the person that brought up this idea. So the ides was somthing I introduced in response to the OP (though I have thought this for a long time).
Now, the level limit is semi-arbitrary. It could be anything really. I chose lvl 10 because that is the point most D&D games end for one reason or another. So, my thought was why not get all your mundane awesomeness in those 10 levels. So you can have your hawkeyes, batmans, etc. in the first 10 levels. Just fill those levels with everything you need to make those characters. And then if you want to play characters more "powerful" you have levels 11-20.
Does that make sense? I am not trying to take anything away. I am suggesting adding on to. In D&D currently (or any edition I can think of), you can't accurately play Heracles or similarly super powerful martials. I wanted to give a path to those types of characters and not have to wait 20 levels to do it.
Also, in this theoretical system, magic / spells would also likely need to be revised too.