What do you think is so secret about the info on your check? You're literally giving it to everyone to whom you write a check.
Crucially, if you give one person a check, you're giving that information to one person (and their bank). If you email it, you're giving it to (potentially) all the people. And I'd hazard that the sorts of people who actually try to intercept emails are precisely the sorts of people who wouldn't have qualms about misusing said information.
In the US, at least, your doctor's office won't send you anything of substance by email for this reason (probably actually because HIPAA won't allow them to by law for that reason). If email isn't considered secure enough for medical information, it certainly isn't secure enough for bank information.
I'm not actually interested in investigating what security has been added to email in the several decades since it's been invented. If banks[0] and the government don't trust it, I'm not about to either.
[0] Mine was aghast that anybody would be so foolish as to send a check image by email. They got the wheels moving to close the account and start rejiggering stuff with surprising alacrity, like "this is what you need to do, and Alice the manager will assist you right now."
Well, them, and every other person you've ever written a check to or who has processed direct deposit paperwork, etc.
Sending check images by email isn't a good practice of course, but it's really not exposing especially sensitive information given the way checks work in the US.
It has cut down a lot on paper usage and made communicating way more efficient.