I don't know if it's just me but when grinding in certain areas in the campaign, I tend to switch between two different parties depending on where I go to. My brain sometimes blanks on who/what combo I use so I'm thinking having the option to save multiple different battle parties would be a fantastic option. There could still be the 15 minute cooldown for switching but I think it would make it easier on folks who often forget, want to try different wolves and companions as a test in the gauntlet but still have an option in a bit to switch back to their main team without having to do more clicking, ect.
Think of it similar to how Pokemon Go has different battle teams when you do raids. Have an option to switch to a different team when needed for the scenario.