The problem is that there's already third party software that keeps track of stuff like this, and there's not really any way to prevent this from happening since it's just reading information that's available on the player's screen.

You can't really use 'memorization' as a power balancing tool for card games like this because as soon as they start using memorization as a skill to design certain playstyles around, it just means people who are able to outsource the memorization to third party software have a huge advantage because they get to play the deck at it's full potential without needing to focus on keeping track in their head. This disproportionately impacts mobile players, who don't have access to this type of software.

And you can say "why don't they just ban third party deck trackers then?", but it doesn't really address the issue because the same thing can be done manually with the click of a button. There's nothing to stop me from, for example, having a second window open on my PC with an Excel spreadsheet that has my deck, and manually checking off when each card has been drawn, played, discarded, destroyed etc.