As a UK salmon fisher I will chip in with my observations on this.
The trebles used very rarely exceed a size 6, usually smaller - often 10s & down to 18s & even 20s on micro tubes for summer lows & warm water.
Because an Atlantic salmon, even a 4 or 5 lb grilse, has a fairly large mouth usually only 1 or 2 points to the treble are sunk - if hooked in the scissors you may get all three engaged but this is in relatively inelastic gristle & it pops out of here with no bleeding.
Because the hooks are at 120 degrees to each other the if two are engaged they don't penetrate as deeply as a single of the same gape going in at 90 degrees to the jaw, but gain the advantage of two points of attachment so spread the load & secure a strong hold - which is why you can get away with a long winged size 8 whereas if dressed on a single you would opt for a size 1 or 2.
As Fred said, the small but very sharp points require little pressure to penetrate & the fish taking & turning with the fly against the drag of the line is often sufficient - particularly with the smaller sizes. Many have very small barbs, but often the anglers will crush these to facilitate an easy release, although in the small sizes the barbs are minute & don't tear the flesh if you use forceps & rotate them out rather than merely pulling them.
Salmon don't feed in freshwater so fish are usually hooked around the edge of the mouth, very rarely is a fly swallowed deeply. If this does occur & the fly can't be retrieved without significant damage then it is best to cut it off & return the fish to the river, there is no feeding to prevent & the fish is still likely to spawn. Only a tiny fraction make it back to sea - if it does the salt water will destroy a relatively fine wire hook long before the fish commences feeding again.
I have never fished for steelhead (yet, still hopeful!) but from what I read I believe they take pretty positively, with Atlantics the take is often no more that then a slight additional pause of the fly as it swings & a small very sharp treble assists greatly with a hook up which may well not happen on a large single.
Mortality from hooking is very rare, providing the angler treats the fish carefully & holds it against the flow to allow the stream over its' gill to reoxygenate the fish. I have actually lost fish hooked deeply on large singles when fishing at night for sea run browns where it penetrated deeply & reached somewhere vital, I have never had this occur with the size 16 or 14 trebles I usually use on my sea trout tube flys which are my usual preference over the large singles.
If I didn't honestly believe they weren't safe then I simply wouldn't use them, but in 25 years I have not felt that this is the case - I don't speak for the overly large trebles of size 1/0 etc fitted to spinning lures & plugs (these are forbidden on the Tweed where the maximum size permitted on any fly or lures a size 4) as these often both penetrate deeply & have over sized barbs, but on the rare occasion I use a spinner I swap these out for a size 6 which avoids the risk.
Those are my findings, others may disagree, & other species which may feed in fresh water may result in frequent deep hooking in which case I can see the need to limit hooks to singles - but I also feel these should be limited in size to avoid the risk of a deeply penetrating point reaching a blood vessel or organ which could increase mortality even if the fish appears to swim off OK but subsequently succumbs to internal blood loss.