Well to answer your questions here's what I thought:
Paper money will be banned entirely?
It will happen eventually, but this is going to be a long process. Its not going to be banned though, but instead its going be eradicated.
How long do you think that happens?
For how long it will take, we don't know the precise time when it will happen, but I guess it will happen soon.
would it work?
Ofcourse it will work, the government need to be changed anyways. Although, there is a chance that it is going to be centralized but all in all, I think it'll be in good shape.
What security and privacy risks would it raise?
Regarding this matter, I think implying the current security of wallets are quite good. Since its true security lies on the person itself, so the fault is not in the wallet.
And how would public and privately issued monies interact?
I'm not exactly sure what you're talking about, but is there any public and private monies?
Future of the paper money remains as it is now, means paper money can't be eradicated by the use of cryptocurrency. But the percentage usage of paper money may decrease, but no body can stop the use of paper money as it is used by everywhere.