One of the biggest grievances in .990 was the inflexibility with builds vs. unique finds. Exotics were created in the spirit of adapting the RNG to player builds. This would approach the problem from another angle by allowing the player to adapt himself to the RNG.
If Kornel really wanted to adapt the RNG to player builds, he would force all exotic/unique weapons to be pistols for AoMr and shotguns for AoSg. Also, I believe exotics were created more because uniques were so rare to find, not to mention that some uniques were far more powerful than others; having another class of equipment eased the system for those lesser uniques and allowed them to appear more often.
Challenges are not so-called because they force you to give up certain classes of uniques. They're so-called because they force you to give up certain classes of weapons, making you explore new tactical avenues with the challenge-specific type. Nearly every roguelike has a wizmode where your scores don't count, but that doesn't prevent it from being a legitimately challenging game. This isn't anywhere near as radical a suggestion as that.
I'm fairly certain only three out of the ten challenges limit you by weapon. (I'd count Pacifism but it's not like you're even looking for items in those games.) As for the rest, a lot of exotic and unique weapons ARE typically resistricted by build: already I've encountered five Cleavers, none of which I was even remotely considering to use because melee weapons are practically exclusive to AoB (and, to some degree, AoMC). On easier difficulties it would take far too long to adapt to it, and on harder difficulties you're set from the get-go lest you be unprepared. You go into the game with a build in mind, and if you're LUCKY, you get either a special weapon that fits the build or a weapon that doesn't require a build to be useful.
Exotics tend to be equipment that are useful in their own situations, regardless of the traits you picked (blaster conserves ammo, assault shotgun has insane reload, laser rifle almost always hits, BFG is...uh...BFG). A lot of uniques tend to be more specialized (three pistols that would still suck w/o SoaG, Jackhammer needs a boatload of shells) that, even if you were going to abandon the challenge, you'd be hard-pressed to find them worthwhile anyway, especially when it comes to ammo types.
Now I'm not against putting this in, I just can't say I would find myself using it. I kinda wish Cleaver could be an exception, though, with more of a chance to drop on AoB and less to drop anywhere else. One time I found it in early in an A100 run and suicided right there.