Bounded Accuracy, a radical idea

I just had a radical idea regarding bounded accuracy and the “Robin Hood Scenario”.  What if Next just allowed players to advance their attack bonus as a choice rather than in ridged lock step with levels.

How this would work is to give the player two or three choices to advance as they gain levels, say Attack, Saving Throws, and maybe Feats.  So when you gain levels you can choose to advance one of those things at the expense of the others.  This would allow those who want to make a Robin Hood-type character to be able to.  At the expense of being an overall kind of sucky character because they would mostly fail all of their Saving Throws and not have and cool tricks just to be the greatest shot of all time.

I do realize that this would create a greater swing in balance, but I think the game can handle it. 

Best of all I think it would create a greater sense of individuality of not everyone had the same to hit.  The key to making it work is to make the decision not an easy one and to make the balanced approach be the most effective choice. 

Now of course I have not thought it through all the way yet, but I think it is a pretty sexy idea.

What do you all think?

Where are the pitfalls?

Is it “just not D&D”?

Let me know.

And please, be nice to me and to others.

the problem with this is that hitting more often will always be the most attractive option (barring a few need-to-have feats that will inevitably show up).

also, the core of the game is essentially done. the designers have pretty much set the current advancement rules into stone at this point.

i will admit that there could be something in the idea that each class's advancement table would offer a choice each time you get a feature (ie. skill trick or proficiency with a new weapon).
Trebor is right. Accuracy increase is so potent a benefit that it becomes virtually no choice at all.
Does that make Dual Wielding a feat tax?