This is true, but if you've already found a better offer with more money and you actually want to make the move, shouldn't you just make the move? Counter-offer

This is true, but if you've already found a better offer with more money and you actually want to make the move, shouldn't you just make the move? Counter-offers seem... too late in the process. Why did the company not pay you that to begin with? Why are they countering now, only after you got the new number? Do you really want to work for a company that undervalues you? The answer might be "yes I love the tech and the mission so this lever is just what I needed" but I think you'll also find the underlying questions problematic.