That's what IUD is for. It's better, IMO, than creating a mechanic completely unique to one class. It would make sense if the class were, say, centered around psychic insights and abilities, but the monk is a martial artist.
It's not unique to that class. Other AC bonuses also apply to most any situation you can think of: size, insight, luck, deflection... And is it really
that hard to implement or understand a bonus that (almost) always works? Granted, monks lose it while sleeping, but I never understood that, or liked that sleeping is grouped with helpless in general. Ever see when Xena (tv show) would catch a blade in her sleep? When I see a monk's "preternatural awareness," that's the first mental image I always get.
Also, that's NOT what IUD is for. IUD is only flanking. Not grappling, not climbing, not anything more than flanking.
Not a feat, no, but fighters (at the least) should get it - UD is the ability to see what's going on around you and react with a split second's notice. Currently, as has been pointed out to me, fighters fail against invisible opponents for precisely that reason. Paladins? Eh... I don't think so, because they rely on their holy power. Rangers? Definitely. A hunter/scout is always alert and vigilant (otherwise he's not a very good hunter/scout). Given that rogues get all kinds of class abilities that fighters and rangers don't, you're not really screwing them by giving a couple other classes UD/IUD - you're just making those other classes more effective at what they do.
1) It's not merely the fact you're giving away key class features that hurts the rogue. You're also making defenses against his only real method of killing things much easier to obtain, when it's already a long list of opponents and items that grant you sneak attack immunity. If a Rogue can't catch you flatfooted, it's much harder for him to fight you, astronomically harder if he's not a melee rogue. I've played a lot of Rogues, aside from enemies with natural immunities, the toughest foes for me to contribute in combat against are other rogues and similar. It's just so hard to sneak attack them!
2) I'm really sick of the whole "Fighters are the weakest class," "Fighters should be good at fighting!" (fighting ambiguously used to reference any little possible incidence that could happen in a D&D fight), and other such arguments. Rogues are not much better than FIghters at higher levels, and absolutely weaker at earlier levels. And their main avenue of superiorit, Use Magic Device as a class skill, is easy enough to get ranks in as a Fighter, especially with splat books. To plunder from the Rogue to give to the Fighter is just plain distasteful, and especially when it's unnecessary -- like it or not, the Fighter is designed to wear heavy armor. UD isn't much use to an "optimal" Fighter anyway, at least for AC. As a form of immunity to sneak attacks, a form of attack that if you follow the suggested population distributions of PC classes the DMG suggests represents a miniscule number of potential attacks...*sigh* If you want a more agile, reflexive, light armored fighter...play something else. Like a Rogue.

Or a Swashbuckler. Who also coincidentally don't get UD. In my Fighter variants, I did give one of them the option to get UD and IUD. But he's also a hybrid rogue/fighter who relies very heavily on dex and dodge bonuses to AC, so it made more sense.