Let's go with "no" for the sake of argument. They probably can't accept an mp3 of me singing my answers, either. But!
If I upload an HEIC, an mp3, a keynote file, or anything else unacceptable... Why doesn't the site provide an immediate "File format not accepted, please upload .gif, .jpg, or .png" message?
According to the article, the software would actually just hang. I think there's room to argue about whether they need to support the default format of an extremely significant platform for students. I think there's room to argue whether they should know enough about INPUT tags to let the browser help with this.
But while we're arguing about those questions, can't we all agree that simply hanging without providing a useful error message, and without giving the student an opportunity to re-upload their image... Is unacceptably poor software design for an institution that holds people's future in their hands?
I don't know about you, but if I were an American college student, I'd now be wondering what else they have kind of slapped together without thinking through graceful error handling?