This raises a question for me. Why are hardware keys so limited in storage? How much extra would it cost to have a secure processor that could access a mass storage device also built in to the key. This mass storage device would of course be strongly encrypted by the secure processor with a key that would be erased at the same time everything else is erased.
I would even go as far and say from a security POV the best security key is the key which has 0 storage. Because in my experience any protocol which injects and stores a secure token into a security key/enclave/whatever instead of deriving it from shared secrets etc. has serious flaws. Sometimes it's fundamentally security flaws (like TOTP). Sometimes it's complexity flaws. Similar you don't really EVER want to share a secure key for HSK/2FA across multiple devices. It means if one device leaks it it's corrupted for all of them. Instead you want a separate key (oversimplified) on _each_ device. Login provider/server side wise the overhead for this is negligible in the bigger picture.