Yes! If you want to make progress, you have to take into account your mistakes and get out of them, so you have to follow your hands!
It is true that you have to think about your mistakes if you want to be a better player. But the way the hand plays out
tells you nothing about your mistakes.
If you have 72 in your hand and the other players have AK and QQ, what do you think if the flop is 772? Do you think you made a mistake by folding?
If you fold AJ in middle position to a big raise from early position by a tight player when you both have medium stacks, and the other player shows AT, do you think you made a mistake by folding?
No, most of the time the player who raised would have a better hand then AT, and you also have many players behind you who might have good hands.
I follow the hand to see if I can gain information about other players. If a player has a straight and does not bet right away, then I know that sometimes that player slow-plays big hands, and I can use that information to help make decisions later.