I'll keep grilling and smoking on the Big Green Egg and use my soon to be outlawed gas stove and cast iron skillet in the house. If you're cooking breakfast for a group the griddle might make sense.
Even if you are only cooking for one or two making stuff like dippy eggs on the griddle is a smidge easier. It doesn't cook any better or different than a nice CI skillet (love my cast iron cookware) but you have lots of room around the eggs for getting the long blade spatula under it and in a quick sweeping motion to not break the yolk and there is plenty of fresh hot griddle space to land the egg after flipping. Same for pancakes. in the 10" Griswold even if only cooking two pancakes they have to be relatively small so when you flip them you don't land one on the other.
FWIW the BGE also works good for skillet cooking. Nice even heat under the whole skillet.
The biggest benefit for me is cooking outside keeps the smells and mess of cooking outside. As much as I love bacon or a good bacala and red sauce I don't want to enjoy the house smelling like it for days.