That would be really cool but for two things -
A: the amount of load outs you can have are already so limited
B: Think of how many blacked out load outs you would have when the event ended
Although, two things I have always wanted in the Battleborn character / skin / Loadout selection screen is the ability to go back and choose a different character after you have made your initial selection (but before you leave the character selection countdown screen) and the ability to select / edit gear load outs on the fly.
Like, create a whole new Loadout from all your gear while on that screen if you have the time.