I'm not an instructor : I've been taught by quite a few of them, though, and I have to say that - just as in business or any other walk of life - if you take a prat and put a collar and tie on him, all you get is a prat in a collar and tie ! It doesn't magically improve his performance.
However, some people feel better about themselves when "dressed up" : and feeling good about yourself is, generally, good for your performance in whatever you're doing.
I personally don't do ties very often (even with a suit), unless I'm going into an environment where it's expected - I'm just lucky, I don't really have to wear one.
However, there are a good many people who - still, even today - see a tie as "professional" business dress. Others, like me, couldn't really care less. I wouldn't turn down an instructor for not wearing one, but there undoubtedly are some people who would. Therefore, the bottom line has to be - in any business - why piss off a percentage of your punters when there's no need ?
FF
