He need shell smash otherwise any flying type will swoop in, outspeed him, and one shot him.
Yeah but before they do that, he will just use Spiky Shield and get off some damage before he switches out. And IF they predict that, then we can just predict them predicting and get off a Leech Seed following with Spiky Shield to get health back AND get some damage off. This would work best against a Physical Flyer, and yes i know it doesn't counter it at all, but at least it's something to do before it gets owned by a Flying typed move.
You don't get totally outclasses because another Pokemon has the same type but one better move. There are lots of other factors to consider. Chesnaught's specific stat spread, move pool and hidden ability can easily more than make up for not having Spore.