And then you have people who lose their cards, or it gets damaged, or who don't want Steam, etc. It's a big can of worms.
To balance the downsides, Nvidia doesn't have to go all in on 'Steam sales', like Sony, who sells some of their PS5 to registered gamers but not all of them.
On the other hand, I don't see the problem with damaged or lost cards. Damaged cards can be treated like guarantees: send in your damaged card and buy a new one. Lost cards on their own are a problem but how do you lose your card? You have to lose your entire gaming rig which most likely means that it is stolen. So send in a copy of your police report. That way, miners will be punished for wrong legal proceedings if they make a business out of 'losing cards'.
I have a baby. I do anything on Steam once a month at best. Crypto miners could pretty trivially make their use cases look like they spend more time gaming than a good 30% of Steam's active user base. This is a non-starter.
Instead of locking cards down, Nvidia could manage the supply. They could sell their cards in cooperation with Steam: Only people with an active steam account are eligible to a new card. If their performance stats don't improve after the purchase, which means they have resold their hardware, they won't be allowed to buy another card.