Well it does start to be a problem if you got a rogue subclass like swashbuckler, who can basically sneak attack (once) every time he is alone with an opponent. Then it might become a bit to powerful. Other than that I see no real big problem, especially since you have to MC which does lower your monk damage output at the other end.In short @Hussar there is no problem, and no downside to changing it.
Monks do get the opportunity to have a third attack but very limited times as opposed to the two weapon rogue attacking twice most rounds. If flurry keyed off something other than a bonus action it could be a problem in opening up too many other rogue action economy options but as it doesn’t...
With all these things my approach is there a way of breaking the game by letting stuff slip. Even if there is, as long as the player doesn’t use it to break the game then I’m fine.
Is it because unarmed strikes are not a weapon and sneak attacks require finess/ranged weapons?
I think normally unarmed strikes are prevented to benefit from abilities that work on weapons mainly because the Monk gets additional unarmed strikes during the turn even beyond Extra Attack. But Sneak Attack is anyway limited to once per turn, so the Monk's Martial Arts and Flurry of Blows won't anyway get additional Sneak Attack bonuses.
If that's how it works, I don't see a serious reason not to allow it. The only benefit is that if the Monk/Rogue first misses with the weapons attacks, she still has a chance for Sneak Attack damage with the extra unarmed strikes, and I don't think it's that huge benefit.
Yeah, see, I've never quite understood why it's okay for rogues to sneak attack with a bow - not exactly a swashbuckling weapon (although it does fit with more scouty type rogues) - but not a club.I mean, of all the weapons that you SHOULD be able to sneak attack with, you'd think a club would fit the bill. But, nope.
So, yeah, I see where you're going with this, but, meh, I'm not going to get too fussed about it.
The truly ridiculous thing is that they can't sneak attack with a longsword, yet Rogues specifically get longsword proficiency.