I don't think you would pass your teacher exams if you took this approach! It's important that we teach our kids how to write properly!
Why is starting written correspondence with a greeting not proper writing?
Unless it is 'Dear Sir', 'Dear Madam' or 'Dear Mr Smith' or 'Dear Mrs Smith' etc then no, it isn't.
Good lord this isn't Victorian England, next it will be only written farewell that is acceptable is "I have the honour Sir/Madam to remain your most obedient servant"