I don't think there's really anything fundamental about them that means that chat has to be interactive and email has to be time shifted, I know many people who deal with chat messages in batches much later than they're sent, and people who will respond to email within seconds. I think that's a ux choice, just like encouraging long vs short messages.
I do like your idea of designating a response time, but it probably requires too much from the sender. It might be that you could train rules on the client that could do a good job of working out how quickly things should be responded to so your client could batch appropriately.
I do like your idea of designating a response time, but it probably requires too much from the sender. It might be that you could train rules on the client that could do a good job of working out how quickly things should be responded to so your client could batch appropriately.