Almost goes without saying that the fusion stuff I like play at home I don't get to do at a gig unless it's my own gig, which I haven't done in years.
I remember posting my big kit from a church gig some years ago, a historic event as it's the only time ever I've used the whole thing when hired. Not a fusion, prog or metal gig, but with a gospel choir that did an anniversary show, hence a lot of styles over a long period in time with their favourites from all their theme based shows.
At that same time I actually used only a 4-piece at home with only hats, 1 crash and one ride usually adding another crashon the right for gigs.
Now, the same big kit is up in the shed again. 3 splashes, 3 crashes, ride hats and china.
To answer the question, though. There's only what's right for the gig and for you. It's common to not bring more than what you need though and people tend to get more serious with concept with age or experience. It's part laziness and part understanding what's important. Sme gigs require a lot of stuff, some don't. Some gigs it would like you were showing off and taking too much space and in other gigs that's wanted.