"If public opinion is worth so little why did the remainers bother to vote at all?"
I wasn't aware of the legal position before the vote. I don't think many of us were. It was understood that the vote was binding, in one sense or another. Not legally, it turns out -- there's no doubt that Parliament, when the question is put to it, should honour the result of the referendum, but that's no excuse to turn aside the rules by which laws are made and unmade in this country.