This kind of exists. Partiko is an app build on the Steem blockchain for android, desktop and ios which has a messenger function build in. You can earn Partiko Points (which can be redeemed for upvotes) by using the app. But only when you post something on the Steem blockchain, not when you use their messenger.
Also, the chat function only works when other people also have an account on Partiko. Otherwise the message will be displayed under the person his latest post.
I like Partiko for mobile phones but on a desktop i use Steemit because i'm more familiar with the interface.
Check it out here: https://partiko.app/referral/niel96
