We experimented with doing something like this on Quizlet, but didn't actually launch anything. We first looked at a lot of the data and doing based on string distance is the wrong approach.
For example, if you type hotmail.de into that checker, it suggests hotmail.fr. Another is ymail.com --> gmail.com. The more valid domains you add, the more (correct) permutations get marked as invalid. We have 20k users with ymail accounts.
I think a blacklist approach is much more solid than a whitelist approach, I just haven't gotten around to building it.