absolutely no question about it, you need choke tubes to shoot well at both trap & skeet. If you hunt with the same gun, you may want them there too, usually tight choke for waterfowl, and not so tight for some upland game
Watch the Olympic shooting events; you won't find a choke tube in sight there nor at any of the world cups. Success in skeet and trap, independently, definitely does not require choke tubes.
As for shooting sporting, skeet, trap, and bunker, there are enough differences in those games that if you're taking them seriously, you should probably have invested in dedicated skeet, sporting, and trap guns. Where the pattern is going in relation to your eye is vastly more important than how big the pattern is when it gets there; you can't break a target if the lead is going in the wrong direction.
The OP asked about trap. The problem with choke tubes in trap specifically is that they modify the pattern, which in turn creates an inconsistency. And as far as trap is concerned, consistency is key. Unless they take each tube out, and pattern it with each load they shoot, they'll end up switching back and forth between chokes to fix a problem that's probably got more to do with gun fit, vision, mounting, or their swing than it does pattern. But, instead of examining their mount or where they're looking for the bird, they just reach for the choke tubes instead.
I agree, you need appropriate chokes for skeet, just as you need the appropriates choke for trap. But if you have those chokes, you really won't need to change them. So as far as trap
specifically is concerned, there's nothing a fixed full over a fixed mod can't do. From 16 yards to 27 yards to doubles, those two will do it all.
Sporting clays is a whole different kettle of fish, but the OP isn't concerned with that just yet... so, save a whackload (seriously, the savings to be had on the used market by opting for fixed chokes is pretty ridiculous) of money by getting fixed full over mod, shoot trap for a while, and then re-evaluate your needs when you feel like expanding into skeet and sporting.