In a vacuum, of course not. In a game where the majority of the information is hidden and a lot of memory is involved, yes, being able to look at your notes of a Celebrity Gift 3 turns later gives you a significant advantage that you wouldn’t have otherwise had (unless you had the skill of memorization). Add on top of that the fact that you’re probably checking R&D a lot and can’t take notes on that. Nor can you take notes on anything you happen to expose, it all adds up which rewards the players with better memory, experience, and knowledge of the game. Is that the right way to do it? Should that part of the game be leveled out by allowing note-taking? I’m not sure, but I think the game would be drastically different if note-taking or card-lookup were allowed.
As for slow play, I have no idea how to help it move faster and enforce better, but there’s no reason to make it slower by adding note-taking as an option.
Speed would be an important skill if they mandated a chess-clock system in tournament play. They haven’t, so it’s not. They have, however, said that notes aren’t allowed. Whether you think that should be a part of the game doesn’t matter. The creators of the game have decided that it is, therefore it currently is an inherent part of a game that has a large amount hidden information and bluffing.