[II2II]

It depends upon what you are trying to visualize. If you are trying to visualize the pattern of the knight's moves, e.g. how to reach a specific square using a sequence of moves, then highlighting the target would be more valuable. The displacement matters, not the absolute positions. The absolute positions are more of a hindrance since it makes it more difficult to generalize the sequence of moves.

[bonzini]

The point is learning to generalize the sequence of moves, and that's why it doesn't give any visual cue.

[gus_massa]

In a real chess position, where the knight must go is the easy part because there something interesting to do there (like capturing a piece). The problem here is that the chessboard is empty, so it's difficult to remember where you should go.

The interesting part is finding the knight trajectory, reading the notation is boring and easy.

(If the point of the exercise was to read the notation, it should be a different game, like clicking that square as fast as possible.)

[JumpCrisscross]

> where the knight must go is the easy part because there something interesting to do there (like capturing a piece)

The aim is to build an intuition for where the knight can traverse without getting captured in N moves. If you can see further into the future than your opponent, you may notice a pattern before they have a chance to stop it. This intuition isn’t fundamentally tied to notation. But having intuition for the notation facilitates it since that’s how discussion and literature will interface with you.