We don't need to speculate; internal emails from the Epic trial discuss the motivations.
https://www.theverge.com/2021/4/27/22406303/imessage-android...
In short, Eddy Cue proposed in 2013 that Apple owning the best-in-class messaging app would be a win, and even mentioned the cost being low. Phil Schiller shut him down, arguing it would remove a barrier preventing iPhone parents from buying their kids Android phones.
That reads like anti-competitive motivation to me. In particular, it looks like tying, where two unrelated products are connected artificially. The wikipedia article on anticompetitive behaviors has a section on tying, and mentions another case involving Apple that bears some resemblance involving iPods being artificially restricted to only playing tracks either from iTunes or direct CD rips.
So I think the anti-competitive angle has some real merit.
The innovation claim, though, I have a harder time with. I don't see how releasing Messages for Android implies design-by-committee. They could just release it, like Beeper Mini just did, but without the reverse engineering part.