Doesn't that violates the whole basic idea of cryptos which was the fact that no one can create it or no one can control it. Moreover transferability too will be hampered with this. Think for example you have one person giving his paper btc to other how will the actual transfer over blockchain take place??
It is the same as transferring the ownership of private keys
The implication being that there is nothing wrong in this on its own. When you give somebody your private keys (and no, you don't necessarily need to know them yourself), quite expectedly nothing gets written to the blockchain. And in fact, it can be a good thing as far as anonymity is concerned. Or bad, depending on which side of the anonymity "fence" (or rather barrier) you are on
Even if you say that there would be some central authority holding all that in blockchain and issuing all paper currency against it then congratulations we are just back in fiat because even the fiat currency today started with this experiment when it was removed from pegging against the US dollar
You don't need a central authority for that. In other words, if these paper bitcoins are backed up by real ones, we will be back to a form of gold standard (let's call it Bitcoin standard)