Thank you for all the comments! Here is some more background.
The player drew once every single day, because he didn't want to have it be destroyed.
There isn't anything about drawing once that makes the deck more or less likely to be destroyed. In any case, some possible things I might do:
Declare that the deck is actually a variant Deck of Illusions, which actually is an item of appropriate rarity, and that all of its effects are illusory.
Adjust its effects to actually be at a Rare level. This has the following changes
Fates: you gain the ability to reroll one die roll, retroactively.
Fool: 1,000 xp, and the deck disappears (I would do this for the regular deck as well)
Gem: one gem worth 1,000 gp.
Idiot: Greater Restoration will fix this.
Jester: 1,000 xp, and the deck disappears (I would do this for the regular deck as well)
Key: Uncommon magic weapon.
Moon: When you attempt a wish, you gain a Divination that advises how to accomplish that wish.
Star: You gain a magic item that grants +2 to an ability score, to a maximum of 20. This item requires attunement.
Sun: 500 xp and an Uncommon consumable item.
Throne: eliminate the bonus to Persuasion.
Vizier: grants the ability to cast Divination, once.
Thank you all! We are playing dnd 5e. Also, I have changed some of the cards abilities to make them less destructive/gift-giving. Also, they can only do 1d4 draws per day.
You must be having fun, since you keep "giving in" to the chaos. Lessening the bad effects does not help a lesson to be learned.
I'm trying to be a dm that tries not to say no. I don't want to be a dm that is the enemy of the players.
Saying 'no' is not being the enemy of the players. In fact, saying 'no' is the job of the DM, you don't need a DM unless things the PCs do sometimes fail.
Note that there is a difference between "You try and fail" and "You can't even try". If the PCs want to attempt something weird, you should let them try, but you're under no obligation to make it actually work, or to even make it possible to work; something should happen, but it's not required that the result be the thing they actually wanted to happen, even if they roll well.
There isn't anything about drawing once that makes the deck more or less likely to be destroyed. In any case, some possible things I might do:
You must be having fun, since you keep "giving in" to the chaos. Lessening the bad effects does not help a lesson to be learned.
You ask for help, but really don't want it.
You could always not use one. I know - not necessarily fun, but...
I'm trying to be a dm that tries not to say no. I don't want to be a dm that is the enemy of the players.
Saying 'no' is not being the enemy of the players. In fact, saying 'no' is the job of the DM, you don't need a DM unless things the PCs do sometimes fail.
Note that there is a difference between "You try and fail" and "You can't even try". If the PCs want to attempt something weird, you should let them try, but you're under no obligation to make it actually work, or to even make it possible to work; something should happen, but it's not required that the result be the thing they actually wanted to happen, even if they roll well.