I'm with Per
I'm moving away from trebles, although I haven't yet had an opportunity to give Loop doubles a fair trial on tubes. But trebles, particularly small ones (#10 and down), can bury all three points deeply in a fish's mouth, which is not good news if you want to release the fish quickly and retain the fly/hook. Doubles do not suffer from this problem nearly so much, though admittedly they can be harder to remove quickly than singles.
I have never liked Drury-type flies except in the small sizes; the longer shanks (#6 and up) seem to create too much leverage, and I believe that on occasion one point can actually lever the other two out. I have no proof of this, but remember well a fisherman in Norway losing a big salmon on one of these flies after about 50 minutes play, having hooked it from the left bank, and during which time the fish left the pool for the one below. The following week a lady caught a fish of about 43lbs in the lower pool, which we fished from the right bank. Her hook was in the left side of the fish's mouth, as you would expect when fishing from the right bank. But the right side of the fish's mouth also had a number of cuts and tears in it, which could not have resulted from her hook. I'm convinced that it was the same fish, and the multiple lacerations in both top and bottom jaw on the right side were a result of the three points of the Drury treble moving around during the course of the fight. It's not uncommon to land a fish and find one point of a treble bent (often not the one attached to the fish), but this seems to happen less often with doubles. Again I cannot prove my theory, but I believe this may be the result of one point being levered out during play by the others.
As for singles, I remember an old friend (now sadly departed) who would sometimes use singles early in the season, but preferred doubles or trebles later on. He maintained that as cock fish grew their kypes, they often develop a gap between upper and lower jaws at the sides of their mouth, and that a single could slide out of this, in just the way that Malcolm describes. Maybe an offset hook would prevent this, but it's interesting to note how they have gone out of favour with trout fishermen over here. 20-25 years ago they were quite common, but you rarely see them now. I can only assume that people came to the conclusion that there was no significant benefit from them. I have a feeling that once you get a hookhold with a single it is at least as secure as a double or treble, because there is no risk of one point acting as a fulcrum to lever the other(s) out. But maybe your initial hookup rate is less. It also occurs to me that Malcolm's single may have slid out of the fish's mouth because it was fishing on its side - Hugh Falkus was insistent that one should check that a fly swam properly before starting to fish. I think the increased weight of 'keel' from the two points of a double increases the likelihood of a fly fishing right way up, which is important not only for secure hooking but also proper presentation (unless, like the Willie Gunn, your fly is tied 'all round' without a defined top wing).
As a final point, I also think that flies look good dressed on doubles, though I'm not convinced that the fish really mind about this!