Saw a video of a thief swapping between shortbow and daggers. Apparently one of the shortbow abilities will teleport you to wherever the arrow hits. So he'd shoot the bow at someone, which would teleport him there, then he'd switch to daggers and slice them up.
As engineer you can do things like switch to the flamethrower kit, drop a firewall, then switch back to your pistols or rifle and shoot through your own firewall to add fire damage to your bullets. Or you could use dual pistols to drop a sticky glue and then switch to the bomb kit to bomb people. Or maybe use the grenade kit to freeze people, then the bomb kit to blow them up...
Anyway, there's a lot of combos that are meant to be for two people to work together with for maximum effect, but weapon swapping gives you some combo abilities that you can do on your own.
It's interesting because I think the goal is "easy to learn, difficult to master". You don't HAVE to switch weapons. You could just stand there and shoot people or whack them with a hammer or whatever, but there's probably something good to be gained if you look for ways to combine your own abilities.
Incidentally, weapon swapping has no delay to it but engineer kit swapping does -- unless you pick up the trait to make it instant.