That's assuming it's a single client on the phone at a single time. Which is wrong. There could be multiple clients on the phone or multiple phone calls with multiple clients.
lol?
What's wrong with
domain.browserdetails.com/somerandomidhere
It allows you to reference it without going into an email. Allows anyone to view it (rather then forwarding the email to 15 different people) and makes it easy to transfer.
I fail to see the reason why email would be better in any sense. It doesn't allow for the same control as one would require for such a service. You also can't organize it as it doesn't come from "client" so if you are looking for it down the road you generally search "Client Name" and it would never turn on.