I should preface this by saying that I love Project Euler--I spent a ton of time there while learning to program. I also am impressed by anyone who volunteers to create something for the community, and invests effort in maintaining it.
However, not storing emails, and thereby giving up account recovery with the explanation that it's about security is a shit sandwich.
My email is .@gmail.com, a pattern I share with millions of people. This is public information. I could spray paint my email address on local bridges without in any way making my email less secure (cops might complain, though).
I understand that some people have reasons to have private email addresses that they don't want released (they'll give them to family, but not the general public). They should never sign up for anything with those email addresses, because the moment you sign up for things, you will almost certainly be entered in a database somewhere, and eventually be spammed or subjected to whatever other bad consequences you're concerned about.
Account recovery is a basic feature of a website (except those that contain data too sensitive to have account recovery), and they're giving it up for phantom security.