I actually really like the idea of rolling for stats, Gamma World-style, in D&D 4e.
The rest of the character creation would be harder to pull off.
The GW 'origins', which every PC gets two of randomly, are clever in that they are all pretty interchangeable. They do this not by being just like each other, but by giving just a few key stat boosts and bonus powers to each player. Rolling a cockroach really just means you get the cockroach's first-level encounter power, defensive bonus and skill bonus, with maybe a couple of minor flavorful extras.
But basically, all players in GW are going to have largely equivalent capabilities and spend encounters using basic attacks or one-offs from randomly drawn cards. Sure, the cockroach can walk on the ceiling, but he's not going to be marking enemies with ranged attacks or healing allies in melee.
By comparison, class choice in 4e determines not just a handful of first-level powers but really affects how combat is played. There's roles, obviously (GW doesn't officially have them although some origins clearly make players more strikerish or leaderish) but within that even the build you choose can have a dramatic effect on what your character does in combat. Are you charging heedlessly into melee? Striking hard and fading away? Raining down death from a distance? Focusing on one big bad or doing minion crowd control? Using stealth to get combat advantage? Class and build largely determine these very significant choices. Letting the dice determine playstyle might feel limiting for a lot of players.
Another problem is that the GW origins are all interoperable. There aren't any two that just don't work together. Now imagine you roll for race and class in 4e, and wind up with, I don't know, Gnome Barbarian. You're going to be at a bit of a disadvantage compared to the guy who rolled Eladrin Wizard.
Finally, any randomly generated character system in D&D 4e would need to adjust for the expected class balance. GW parties don't need a healer. D&D parties do (not absolutely, sure, but it really helps!).
GW 4e removes a lot of player agency from character choice but makes up for it by giving players the creative challenge of figuring out how to play a robotic plant. By contrast winding up with a goliath psion isn't funny, it just sucks. Add in stats that are at least partially randomly generated and you have a recipe for No Fun.
I'm not saying that random D&D 4e chars can't be done, just pointing out some of the challenges that need to be overcome. One partial solution that springs to mind is to eliminate racial stat bumps and instead tie the stat bumps to class (ie, all fighters have +2 to str and con, even if they're halflings).
