Definitely this group has more common sense and familiarity with the use of email than most of your students.
First of all, if you have a preference for a given format, information included in subject line or in the text, you should say so. Students are coming from different places, they cannot just figure out of your expectations or preferences.
Second, emails are not letters. The common way of professional emails is similar how the said group used it: brief, contains only necessary information. Most text on professional writing clearly discourage all kind of "Dear XY", "Best regards" and similar. Wishing you good weekend of rehearsing that the attachment is an attachment, and indeed it is what you think is rather unnecessary.
Off course you can have a personal taste different, and you can ask your students to accommodate, but don't expect that your rules are universal or known automatically by everyone.
To answer comments:
Indeed, empty mails are a little extreme. However the closes format to an assignment submission is a memo, and memos does not contain salutation, greetings, or any superfluous "best regards", "is your dog happy?" etc or signature. In other words, memos does not contain anything that OP is explicitly missing.
If one has other preferences, she/he is free to write a guideline or communicate that. For example a page like this: http://faculty.mccombs.utexas.edu/kristie.loescher/assignments/memotips.htm
Comment along the line with Nate's answer, and using his example:
Just for the sake, imagine a similar homework assignment on paper. Do you expect a printed letter like "If it would be a homework assignment, no one would expect an extended intro with "Dear Sir, How was your weekend? I hope you are in good health and enjoy the chirping birds of the Spring. Let me introduce you my solution for the first problem you kingly asked us to solve:" with a big "Should there be any question feel free to contact me. Sincerely, (huge, hand written signature)" at the end? Would you frown upon students who are listing only the answers, no greetings, no salutation as unprofessional and rude behavior because they do not follow standard letter formats (or what you think standard)?
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