I think it's because you can't "equip a class".

You can equip a tool or equip a gearset, and you'll change to the associated class as a result, but those aren't universal things that can be put in the crafting menu for everyone.

Possibly they could create a system where you designate a gearset to be associated with each crafter and then the crafting menu can auto-equip that gearset for you.

For now, though, I think you might be able to switch classes without leaving the menu if you've set the gearsets to your hotbar. I set those up a while ago though I tend to forget they're there, so I can't remember whether you can switch while in the crafting menu or if it just saved opening the Character and Gear Set menus.