It may be not a bad idea to solve the problem of scaling Bitcoin. I don't see much harm in banks abusing this and issuing more "bitnotes" than bitcoins they have in reserves. If bearers of bitnotes can no longer redeem notes as advertised, that particular bank will go bankrupt and be purged from the economy. There is no central bank to bail it out that can quantitatively ease to infinity. The damage will be limited unless the inflationary settings of Bitcoin itself change
I think that you are sarcastic
If banks start defaulting on their bitnotes (I will use this term to avoid confusion with paper wallets), they will be scamming on people just like any other Bitcoin scams out there. To say that it wouldn't hurt Bitcoin is basically equal to saying that scams don't hurt Bitcoin either, which is obviously very far from truth. People even tend to blame Bitcoin itself for facilitating the spread of such fraudulent schemes
Yeah, it seems impossible and not realistic right now but maybe in the future there is someone or a bank that makes it come true, we don't know yet how technology lead us, an innovation is always needed. There are a lot of homework to do if paper bitcoin will issues, the most important is about security of private key and forgery such as others had mentioned.
The issues you are talking about are not very different from the ones faced by any web wallet. In fact, they are pretty much the same