There is one simple solution though, what if you mint physical coins each with QR code that represents bitcoin address

Private key of all addresses on coins may or may not be held by central organization ie. government thus having the ability to make coins worthless if bitcoin is sent to another address. Central organization can verify if their minted coins are being counterfeited.

This approach has some unique properties:
- coins that stand for 1mBTC can each have 1mBTC on their addresses. No one is silly enough to send for example 1BTC to 1mBTC coin address. That would make him directly send 1 BTC to central organization
- coins have physical form which means no Internet or electricity is needed
- can be traded like exchanging cash with no waiting time at all to for confirmation making it possible for everyday use
- central organization has the ability to retrieve coins in the circulation by simply spending amount from coin address
- anyone can check if coin has the amount of BTC that it is claiming it has
- maximum market cap of all coins in existence is defined by BTC market cap which controls deterioration of minted coins via inflation (no inflation that steals value from holders can be implemented, only minting more coins that are directly pegged to BTC value)
- central organization that mints the coins do not need to be centralized
- private key of minted coins can be destroyed which means that destroying coin you lock forever BTC value attached to it (making it more deflationary)