Sure, the inductor conduction losses would go away (and that's a substantial improvement!), but I'm not sure what you're talking about with regard to reducing switching time. I don't think the MOSFET gate drive is limited by the wire that connects to it.
It isn't but the capacitor that is sitting on the far end of that circuit is limited by how fast you can pump current in or out. And if your current can go up considerably then the capacitor will charge that much faster and so your losses will be smaller because for the same 'on' duration of the MOSFET you can move more charge. Clearer now?
The output capacitor in a buck converter is charged through the inductor, whose current is continuous. I think we must be talking about different things.
