Most people have wealth held in real estate, stocks, bonds, cars, businesses, retirement accounts, etc... and a comparative few bucks of cash.
So even if you take the view that it's compound annual interest to the central bank, you're only paying it on the amount of money that you float as cash and non-investment accounts. And in return you get a managed, reasonably predictable currency.
Could be taken even further to view it as a regressive tax... Chances are if one can afford to hold your wealth as you described, she is not living paycheck to paycheck.
Especially relevant in an economy where many may have been forced to drain their savings and now indeed are trying to save raw currency to re-establish.
Yeah, when I get older I'll buy stocks, maybe buy a house, etc. But I have a decent amount of wealth, and I'm "paying interest" on all of it.
If interest rates weren't in the toilet right now, I'd look for a savings account paying real interest, a CD, or something of that sort. Luckily the "interest rate" levied on cash is low right now, so it's not worth it to me to bother.