[Rehashing an old comment]
In the math department, we had a Moodle the students in the first year of my university in Argentina.
When we started like 15 years ago, the emails of the students and TA were evenly split in 30% Gmail, 30% Yahoo!, 30% Hotmail and 10% others (very aproxímate numbers).
Now the students have like 80% Gmail, 10% Live/Outlook/Hotmail and 10% others/Yahoo. Some of the TA are much older, so perhaps "only" 50% use Gmail.
The difference is huge. I blame the mandatory gmail account for the cell phone.
So, checking only @gmail.com is too strict, but a first fast check for @gmail.com and later the complete regex may improve the speed a lot in the real word.
Maybe I am old, but I like to keep as much communication as possible going through the university email. It just feels more official somehow.