Any hook is only as safe as the angler who is using it - or rather the angler who is trying to take it out of a fish they have caught.
I am a fishery manager and insist on barbless hooks where I am likely to have inexperienced anglers i.e. on busy day ticket waters.
Generally speaking, I believe barbless hooks cause MORE fish mouth damage than barbed when playing a fish and that barbed hooks cause more damage than barbless during unhooking by an inexperienced angler.
I watch the evidence very closely and have for a number of years and am now seriously contemplating banning BARBLESS hooks on RMC's big carp waters such as Horton, Nutrabaits Yateley, Sutton, Wraysbury, Abbotts etc.
Personally, I will not use a barbless hook in any circumstance other than when pike fishing.