Personally, I think the devs wanted to back off the condition overload of 3.x & 4.x, and went a little overboard in some instances. In 3.x, undead where immune to criticals, thus sneak attack was useless against them and rogues rendered much less effective. So now that restriction is gone, and you can now sneak ghosts. I could see arguments for this not being the case though.
In 5e, it seems the devs have decided that the Stunned condition should be almost the soul province of the Monk, Wizards have to wait until the 8th level Power Word Stun to gain the effect, and that spell isn't all that for its level (I guess one of the effects of Divine Word as well, but that is even more rare). I believe that is the only ability available to PCs outside Monks that bestows the stunned condition, barring some magic item I'm overlooking. I'm not sure how many Monsters inflict the condition, but I don't recall many doing so. So, its almost as if the condition was put in the game specifically for Monks, given the rarity of it outside the Monk class.
So I suppose putting immunity to Stun would be a direct setback to the Monk, as so few other classes and creatures would be affected by such a change. To me, that speaks of an over reliance on the condition by the Monk class, as I'm not sure why there cannot be other effects that impose the condition. I don't think it would be too bad if there were some rare creatures that had immunity to the Stunned condition, such as Constructs, but then again I don't see why the condition should be almost the soul province of the Monk class anyway.