I've got both but would rather use the pro controller. Is there any reason I would want to use the gamepad over the pro controller?

Item Switching with the gamepad in your hand would probably be a bit faster, as all that happens on the touch screen Going fast, is literally managing your inventory without too much timeloss.

Second reason, the gamepad has Gyro controls, whereas the controller has not. It's not a necessity, but in my opinion, it definitely helps

If you very much prefer the feel of the pro controller, but want the time save from item switching, you could use the pro controller and have the gamepad next to you for quick item switching. Same thing with gyro controls. When those sections pop up, you can use the gamepad, and switch back to the preferred pro controller after! There is no penalty for this (you don't have to into options or do anything extra).

Switching controllers in the middle of a run in order to use gyro does require going into the options. The only times switching controller is fine is during savewarps. Same with turning gyro on and off with the gamepad which requires going into the options. The gamepad is the fastest controller thanks to the gyro timesave in theory, but in reality it doesn't matter. As long as you use the gamepad to equip items on the fly you will be fine.