Monero has the concept of private view key and spend key. The view key only lets you check balance without loss of privacy. View keys can be printed as a mnemonic seed (a set of meaningless English words). Would printing of view keys mnemonic not be equivalent to this? With the added advantage that printing is not centralized?
I don't know enough about Monero's construction; wouldn't this be trivial to counterfeit? Can you use this key to ultimately transfer the funds?
this is full text of a View Key
A keypair specific to Monero. The public part of it makes up the 2nd half of monero address, and is used by the sender to generate a one-time stealth address to where the funds are actually sent. The owner of the wallet uses the private view key to scan the blockchain and find the funds sent to his address. At the protocol level, the sender performs an encryption with the recipient's public view key, and the recipient attempts to decrypt all the outputs on the blockchain to find the one belonging to him (where decryption was successful). For audit purposes, it could be shared with the auditor, along with the signed key images to prove the balance of a wallet. Sharing only the view key would enable the auditor only to see received transactions, but he wouldn't be able to tell if any funds were spent, so he couldn't know the actual balance.
In the trivial case that each kong is a wallet - a view key would actually show the balance.