Email's maturity by the time that businesses all came online pretty much guaranteed it as the standard for business communication, and personal use was just a small step from there.
Expecting 20s RTT for email is a modern phenomenon, when you could expect replies on the timescale of days before.
The closest attempt to a standard for IM is probably XMPP, which providers have pretty much all ignored in favour of lock-in to their respective platforms.
I think the whole point of having email is for communication where you'd expect responses on this timescale (for reasons outside of communication protocol used). Some questions just take time. The immediacy of instant messaging puts pressure to respond quickly.
Even for personal communication, if I want to write a longer letter, I don't get to do it every day.
On that note, none of the current IM clients are suitable for long messages. Even your comment is too long to be comfortably sent in an IM. There's a whole infrastructure around emails that make them suitable for long messages: drafts (so you can work on an email over the span of days), editing/formatting, and so on.
Then there's flexibility of the message being a unit of communication, rather than the chatroom. Your response can selectively quote parts of a message, being sent to a a part of the group, be forwarded. It's not easy to do with IM's.
But in the end, I do think that the non-instantaneous nature of email is the reason why people use it: IM's for short, fast responses, and emails for "...I'll answer it tomorrow".
And IM address is more or less private and restricted - you need to approve other party in order to send you messages.
And this, not the latency, makes the difference.
People are using Skype for example in "email mode": sending messages even when they know that contact is offline - it will be read later anyway.
Yet there are more differences:
1. Uniqueness of address. You may have tons of email addresses. But other party cannot be sure what you are reading any of those. While in IM you have one address in their particular namespace.
2. Consequence of #2: Most of IMs keep conversation as single tape - you know that if you or your correspondent did ever say something you will find it in that particular place - on that tape.
3. More or less guarantied delivery and corresponding UI feedback ("his/her LED is green!"). If you see "message delivered" then it in magnitude of times is more probable that your correspondent have or will read it. With emails it is more like a gamble. How many times we heard advices to check spam folder to find someone's message?
If desired, you could require approval from the recipient to reach this IM-level visibility if sent by a stranger, with unapproved messages appearing in the normal email box (sorta like FB does with non-friends). If someone is sending you too many, you can de-approve them, and you'll just respond slowly like email. The de-approved sender doesn't need to be told they have been de-approved, and the fact that we don't always reply instantly to IMs provides plausible deniability.
That's one of the points. I can publish my IM name but I will receive messages only from those recipients whom I will approve.
Publishing email address ... well that's the main reason why we cannot live without services like GMail - to filter out spam.
Email, for network connected machines with delivery direct into the recipients inbox (this is how SMTP works if both sides are network connected and online, and in fact was how SMTP was designed to work for connected systems) is also sub 1 sec delivery latency (at least for normal sized emails, 2G of attached photos will take a moment to ship over).
20 seconds for delivery of email (ignoring intermittently disconnected systems, which email still supports) is only because most email clients work in a polling pull mode from a central server, and the polling delay in the client is what adds the apparent latency. It is a result of how most clients are designed, not an inherent built in latency of the system.
Was any of this predictable? Or could we just have easily ended up with everything fragmented, or everything a uniform standard, conditional on flipping a few minor historical events? The potential of very strong path dependence for the quality of equilibrium services is very disheartening.