Text messages are very slow, and nobody minds. People on iMessage don't see the difference.

It's more a metter of perception. When you click on a mail, it takes a lot of time to type, then your UI have a delay to say it's sent, then you have this time taken by many clients to move your mail to the proper folder. But a proper mail-chat client would just make the message appear as sent, then to all the stuff in background, and you would just not see it slower than other chat. The time people take to answer you message is usually the bottleneck, not the network.

This application appears to do pretty much what you're suggesting:

https://play.google.com/store/apps/details?id=com.pingapp.ap...

Unfortunately, my colleagues insist upon using Skype instead of email, apart from the few I've persuaded to use Google hangouts instead.

people on iMessage see the difference between SMS and iMessage ALL THE TIME! I have friends that refuse to respond to my SMS messages in iMessage, since I have an android phone - We use FB Messenger to communicate instead.

Users are extremely sensitive to latency. I would ditch a chat client with any real latency in a heartbeat.

Would email providers block chat-over-email after you sent 1000 or so messages in the space of an hour?