I don't know about XII or XVI 'cause I haven't played enough of them but XIII didn't, well unless you count the Dreadnaught thing you get to do once in Chapter 4 or the Chocobo treasure digging thing on Gran Pulse.
XV had a few but then again that was one of that game's issues in that there was a shit ton of side content while the actual story left a lot to be desired. X-2 had a bunch of mini-games as well if you want to count sequels.