That's exactly what they tried to do with Hangouts, which is why it was also the default SMS app before they gave up and released Messenger instead.
The problem is when you release any new app to become the "universal" solution you're really just creating yet another app for people to deal with.
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Where Google failed at was the art of subtlety. They should have implemented it in the messages app that the majority of people are already using. Hangouts acts and feels more like a 3rd party app vs a feature ingrained into the Android. Why couldn't Google just implement user's Google+ accounts into the Messenger app, and keep it simple? Instead they created the cluster $@#! Hangouts, that wants to become a hub for everything Google.