The demand is simply not there. The feature has been around since 2009 (on Palm webOS, that was the main attraction of the OS), but it's never joined traction.
One of the main reasons, most people find it complicated (because they've never used it) and so it goes unused. Even if it's a better solution, simplicity > complexity.
Which is easier to use: an app that works out-of-the-box, or an app you have to configure with your own messaging service?
Even integrating a simple messaging service has been attempted on all major devices (iPhone has iMessage, Android had Google Hangouts, Windows had Skype, Blackberry had Hub).
Every single one except Apple's iMessage was removed in less than a year. Users simply didn't understand it.
Apple only succeeded because it worked seamlessly and transparently (most users didn't have to even enable it, it was always on). The feature was never "advertised", in fact it was harder to turn it off than leave it on. Basically they fooled users into using their product, therefore getting around the complexity/ease-of-use problem.
And then there's the branding/additional functionality, which others have already pointed out. Facebook, Kik, iMessage, and more have figured out how to monetize messaging, with microtransaction for added features.
In order for standardized messaging to become normal, users will need to understand WHAT it is, and WHY they'd want it. And the only way to do it, is to explain it to them, in a way that makes them WANT to use it.
The standardized system additionally needs to support all features, such as full emoji, bots, security, anything a service may want to implement.
If the demand is there, messaging services will follow it to avoid losing users.