I do not think an outright ban is necessary for these birds. From a European point of view, collecting them from the wild is already mostly illegal, and given that tube-noses, swifts, frigatebirds and swallows* have hardly any meaningful population in zoos at the moment, I think that the current legislation is more than sufficient. A ban would only make it harder for zoos to (temporarily) take care of rescued individuals.
* The one exception in Europe in can think of is Barn Swallow, which is kept and bred with reasonable success in a handful of zoos. I have only seen the aviary at Rotterdam (they were signed in the Okapi aviary, but I have never seen them), which provides reasonable space for them to fly. While I am not a fan of swallows in aviaries, barn swallows seem like the most reasonable choice (given that they perch far more often than, say, house martins, and also sleep while perched). Again, not a great fan, but it is not much worse than the way raptors are usually kept.