Ok, I played a Monk a bit the other day. One run I got Martyr Wraps, and the other run I got Venom Dagger.
Venom Dagger was sort of useful on Monk, but only on par with Fine Sword as far as I could tell. MW was flipping God tier, on the other hand. It just feels wrong when a single class is the best use case for two items, but one is God tier and the other is just kind of good. Especially when VD is mediocre or worse otherwise, except for the rare case when you have tons of gold and a small item slot. Monk essentially gets double benefits from VD, so it should be amazing... The only thing I can think is that they didn't want it to stack too much with Tikki and/or Gorgon...