This doesn&#x27;t scale well and is impossible if you want to send any media. If such an app were to become as popular as iMessage, it would need to handle 200k message per second. I can&#x27;t download so many messages per second on my phone. You could send blocks with 2000 messages but you could easily be deanonymized (look, out of those 2m messages, he requested 5 blocks with the same author. I think they talk to each other). Don&#x27;t get my started with kilo to megabyte big images. 
If you would not want to scale the app, you could also be deanonymized because you&#x27;re talking with a niche that has less then 10,000 users.<p>I wish there was an easy solution to this problem but we already see how badly Bitcoin scale and there are great articles why Bitcoin with its current design can&#x27;t be used in the real world simply because the block chain has a pretty low limit on transactions per second.