Oh, this is so terrible. I hate this approach with a passion. E-mail is NOT INSTANTANEOUS. It was never meant to be. It happens to arrive quickly for most people most of the time, but you should never, ever, base a service on that. Many systems have greylisting in place: a new sender gets a 4xx reply, and is allowed through only on subsequent retries after a pre-set time period. This is often as much as 30-60 minutes…
Email has been nearly instantaneous for me for the past decade or so. Either it arrives in a 30 second window, or never. Usually 2-5 seconds.
Joking aside, email never coming is a pretty common occurence for me on new services, especially small orgs (local clubs, small merchants)