You’re right that we don’t need to, but mathematicians can use this method to prove that two infinite sets are the same size. This is how we know that the infinite set of whole numbers is the same size as the infinite set of integers. We can also prove that the set of real numbers is larger than the set of whole numbers.
I’m not quite sure how else to explain it, so I’ll link a Numberphile video where they do the demonstration on paper: www.youtube.com/watch?v=elvOZm0d4H0&t=19s . Here you can see why it’s useful to try to establish this 1-1 correspondence. If you can’t do so, then the size of the two infinite sets are not equal.
People on Lemmy like to argue and I’m taking a strong stance on something here. With those two things in mind, I’m expecting some level of push-back. (Which, admittedly, has yet to materialize.)