I do not think swans are very good at flying. They are very different from most big birds. Very large birds like eagles, storks and pelicans try to avoid flapping as much as they can. They find thermals or other updraughts of air and gain height with wings that are almost still and just need adjusting to take account of air currents and their intended direction. Swans never soar and so do not look for thermals. If they are flying then they are also flapping. I suspect that they are aerodynamically incapable of staying airborne with still wings. On the whole the White Pelican is slightly heavier that the Mute Swan and with a slightly longer wing-span, but I suspect that it is the shape of the wing which makes all the difference to whether the bird can soar or not.
This is borne out by the moult. Most birds moult their flight feathers a few at a time but can still fly well with the remaining feathers. Swans, geese and ducks are different. They moult all their flight feathers together and become flightless for a few weeks at the end of the breeding season. This is a big disadvantage during the moult but it does at least mean that they can fly reasonably well with a flapping flight during the rest of the year.
Swans do seem to find it difficult to manoeuvre at short notice. If they do not see overhead wires until they are close, they sometimes collide with them usually resulting in the death of the bird. Another surprising thing about swans is that they always fly with their necks extended, never retracted like herons and pelicans. This means that they have to keep all their neck vertebrae in a horizontal line throughout their flight. It might have been thought to be more comfortable if it were retracted. Part of the answer might be that its head is not very heavy. I did once have the skull of a Mute Swan and really it did not weigh very much. I imagine herons and pelicans would have much heavier bills to cope with their methods of feeding.
Although there are a few problems in understanding their flight, it is always good to see a flying swan.