"By the same logic we shouldn't bother having a general election, because the people have already had their say, and it's not like anyone ever changes their mind right?"
According to remain. Think about it. We vote in a general election and the winning party gets in to implement its policies. Then after time to implement policies we have another election. So far we joined the predecessor of the EU which morphed into the EU. We voted to leave and yet before policy is implemented, before the result is acted upon the losing side are crying 'no I want another vote so people can change their mind'.
We would never have a new government if we did that because the situation you said would be.