Tyvek is an air-infiltration barrier. Air (hence, moisture too), is allowed to pass from 'inside' the house to the outside whist preventing air from the outside (hence, moisture too) from getting inside.) Since it 'breathes' one-directionally, then I'd suspect that if there was going to be any mildew, it would be on the OUTSIDE 'side' of the wrap only.
Now, I'm sure one could create 'conditions' that would be ripe for the growing of mold and rot but when installed properly, it shouldn't be a problem (for the aforementioned 'reason(s)'.) A DIYer may not 'know' what the purpose of Tyvek is and, hence, use it for something it wasn't designed to do. (Like a vapor barrier.)
In short, assuming it's properly used and installed, I don't see any problem. Others may have more to say. (I can't speak from having done any 'research', but at the same time, I haven't heard or read that it failed for reasons like you've asked.) My best to ya and hope this helps.