A recent bug fix removed the ability to rearrange prize cards with Azelf’s ability because it led to some bugs. What makes this a bad approach is the fact that being able to decide exactly which prize cards to take for the rest of the game was a massive part of what made 2010 skillful. A better solution, if just fixing the bug was too difficult, would be to let a player who has used Azelf peek at their prize cards whenever they want to for the rest of the game. This is what 2010 players do in casual play in-real-life, while in more high-stakes play they take out a notepad and write exactly where each card is.
You can still choose which prize cards to take. This doesn’t affect the gameplay of any formats azelf is legal in. You can just use a notepad like you said instead of rearanging them.
Or you can just take a photo of it like I do