Here's a simple example where the certain knowledge of an opponent's hand comes in handy:

Player 1: "Hey, Player 2, I'll trade my wheat for your brick."

Player 2: "I don't have a brick."

Player 1 knows that Player 2 got two bricks and a wood 3 turns ago, and he bought a road. So the one card that's left over is a brick.

Player 1: "OK, I play a knight development card, I move the robber to your plot, and I take your card. Lo and behold, it's a brick!"

You'll get the same effect by just looking at the board and noting who has the brick production.

No, you won't. It's entirely possible to have brick production but no brick right now. Have you ever even played Catan? This is basic stuff.

And by tracking the cards you’ll have a better model. You seem to be agreeing that this information is useful

I'm not, really; the normal mode is that you offer to buy something and you get it or not. But if you want the information, it's publicly available in high but not perfect fidelity, making tracking hands even less valuable than otherwise.

So do you show everyone your cards to speed it up because you think them knowing offers nothing useful?