I'm a NH citizen.
School teachers are not professionals. They're not professionals not because they don't have a requirement for specialized training, a mandatory 4 year degree ensures that. They're not professionals because they do not belong to a regulatory organization capable of policing their own. They are not professionals because society as a whole no longer defers to their judgement; instead communities have stripped professional decision making ability from teachers.
Which means teachers are just common workers. And an enhanced dress code for them is no longer appropriate for their social station.