Yes, but MM did not use to do that and they changed it because it was too good to be able to walk around with Kill Clip (essentially) in your pocket. That is also an okay way to balance osmosis, but both Ace and pretty much any weapon that can roll osmosis don't solely rely on a singular perk to make them good, whereas Tarrabah is only really effective when Ravenous Beast/Bottomless Appetite are active.

I can understand, my biggest issue is the ghost and maybe sparrow ones. Pull it out to check bounties and gone