Does a game like this exist?

[GreyLord]

In "customization", do you mean fluff, or crunch?

Old School Hack allows you to customize to your heart's content, but that customization will largely be fluff - for example, you can have any weapon you want, but it will be mechanically identical to other weapons of its same general size. Huge frikkin' axe is the same as huge frikkin' hammer is the same as huge frikkin' sword. As far as the game is concerned, a bow and arrow is the same as a wand of magic missiles - a ranged weapon is a ranged weapon, and that's all.

I have been surprised how often the lack crunch difference ends up not mattering much to the player.

Along those same lines, an incredibly LIGHT RPG was called Fighting Fantasy. It had 3 stats which were Skill, Stamina, and Luck. Another arena of Magic could be a factor depending on what type of character you wanted.

However, much of everything else was fluff if you wanted various characters. Just like above, add the fluff and whatever you wanted.

The Fighting Fantasy Gamebooks used this system. You can see from them that they had characters from everything from your standard swordsman adventurer to Starfighter Pilots zooming through space.

If it's too simple, then they have Advanced Fighting Fantasy which has more options, but with more options comes a few more restrictions as well. It's still very customizable, though it can be a tad broken at parts too.

Nice system if you can find the books. The Fighting Fantasy RPG and/or Advanced Fighting Fantasy

 

[Mark CMG]

Along those same lines, an incredibly LIGHT RPG was called Fighting Fantasy. It had 3 stats (. . .)

So, too, Prince Valiant The Storytelling Game.