I mean, there's an easier way to set a negative interest rate on cash. Periodically select X% of the circulating serial numbers and declare that they're no longer valid currency.

In effect this makes X% of cash "burn off" every period, and allows the monetary authority to set any negative effective interest rate that they want.

This is by no means an endorsement of negative rates. But if you're going to go down that road, it's a better scheme than just trying to make holding cash too much of a pain in the ass.