I believe this is because both Flex and Stax support NFC, as the backup method used by Ledger requires such communication channel. I’m sure if their other products supported NFC, they would also extend this backup to those devices.
they could have developed Ledger Recovery key to be compatible with hardware wallets from other brands as well.
I think this is highly unlikely. If it were possible, it would imply that other wallet manufacturers have left open access to SEEDs on devices they've produced, which would be serious security flaw. As I’ve mentioned in one of my previous post somewhere here on forum, SEED must be backed up only once, right after it's generated. Whether the backup is done via NFC to smart card or through another secure method, SEED must then be sealed inside SE and never exposed again.