I'd like to see more frequent outbreaks in the game, especially when there's no event going on, between events. For example, the gap between the Easter and Summer events is always quite long.
Whenever there were outbreaks with Alolan Forms, it would bring a lot of players. I remember there was once an Alolan Rattata outbreak on Route 2, and a friend ended up catching a shiny one.
Of course, the ideal would be to make new Pokémon available during outbreaks, but there are some Pokémon that have already been released and are no longer available anywhere that I'd like to see in outbreaks: Rockruff, Dhelmise, Sandgast, Skovet, Wooloo, and Falinks.
There are also Pokémon that are available in the game but have very poor spawn rates, like Purrloin; it would be nice to see it in an outbreak.