Good idea but is a federal crime to mutilate a bill. I prefer the way to have own paper money as paper wallets, just as casaciuos coins and bills, only with multisign addresses.
Yeah, the best solution would be to create an organization with reputable members who would provide their own public keys and print its own currency. Actually I kind of like the idea of repurposing a national currency. There's something poetic about this. Consider the Venezuala Bolívar:
If I was a Venezualan, and I'd watched the value of my 500 Bolívar bill decrease 46% overnight (http://wealthcycles.com/blog/2013/02/08/venezuela-devalues-almost-47-too-late-for-many) I might take some satisfaction from "guaranteeing" the value of my bill by adding bitcoins to it.
Do I understand correctly however that this is almost a "proof of burn" type of valuation? The bitcoins allocated to a bill are *provable* yet *unspendable*?
Thats correct. However a centralized institution having several public key holders could theoretically create redeemable bills. People using imprinted bitcoined bills would have to trust the "board" of this institution that they would not arbitrarily remove the bitcoins from bills unless the bills are also physically destroyed.