For this feature in particular, I can think of a very obvious reason: it would change the gameplay and upset the balance of the game, quite a bit.

At the moment, it is part of the challenge of the game to work with limited information and keep track of the information revealed. With the suggested history that would obviously change.

Not to mention, not everyone can read and process information at the same speed. Players with dyslexia or players who speak English (or any other game language) as a second language only would be disadvantaged if the game changed to include history.

So I don't think you could see this change as an improvement without drawbacks. And thinking about it, it's kind of weird Showdown allows the full history to be shown where it's supposed to be a simulation of the game which doesn't show it.