My understanding is they also ban third-party text message applications, but I could be confused on the details.
It's not anticompetitive to never allow a third-party text message application in the first place.
Messaging apps that compete with iMessage are plentiful and Apple doesn't get in their way. You can also disable iMessage with a toggle on the Messages settings screen (it's well "above the fold" for me, fourth entry down, on that screen, it's the first thing they show other than security/permissions stuff for the app)
On Android, yes. Not on iOS.