They did. Well, sorta. Google adopted RCS[0] for Android (and even added end-to-end encryption to it), and despite mostly only being pushed by Google, is an open-access protocol that any carrier (or company) could implement themselves.
Because Apple would sue them. It’s generally not kosher to make a custom client for someone else’s proprietary system. Little players sometimes get away with this, but when large corporations do it, they get sued.
Microsoft tried this with YouTube in Windows Phone. They got shut down by Google. If they had persisted with shipping it anyway (bypassing the block somehow ), they doubtless would have been sued.
My bad, I meant rolling out their alternate protocol.
If I use an iPhone with other iPhone users, the default messaging app simply just works. Why not replicate the same experience for Android users? Competing by creating their ecosystem where the green bubbles are the premium experience and the blue ones (for iPhone users) is the fallback to legacy SMS?
Google doesn’t want to build that. They have publicly stated as much in the past. At the time at least they are pushing for improvements to the MMS infrastructure/protocol to support iMessage-type features.
But also just because they build an equivalent system doesn’t mean anyone would move to it. They tried that with Google+.