I would also like to see this feature, but I believe the current set-up for the pet events is that it remembers the last team you utilized either against the last “boss” you fought for the pet event, or for each individual pet itself. I’m not sure which way it is, but I know I’ve had different team set-ups automatically plugged in for many of the pet events I’ve participated in. As I said, I don’t know if it plugs in the last team you used based on the Legendary you fought last, or the pet itself.
So, basically, when it is a goblin enemy pet event, it automatically plugs in my Gob-Eater team. And when it’s some of the other teams it plugs in my All Goblin team, or my Justice League for some of the others. I never have to change them, because they’re already put in.