I think you are correct in most respects, but Butler compared to Tuck and Stewart is fundamentally different - they depend on speed, and three point shooting, and motion on offense, and were capable of defending guards and wings on defense so they could switch on every screen. The team got into those defensive and offensive rhythms, and suddenly you had a big, back to the basket, post up kind of center in the game who did not have the quickness to defend 15+ feet from the basket, so offense which depended on 5 players threatening to drive or shoot from distance, and defense that depended on Moriah switching with Stewart and Tuck on every screen, was asked to find a compromise. It didn't look pretty most of the time.
A comparison would be the struggles MN had last year when in mid-season they completed the trade for Sylvia Fowles - she ended up being the finals MVP, but the team really struggle for the 6 weeks or so prior to the playoffs, figuring out how to use her strengths and cover her weaknesses - and that was a very mature team and a very mature player.