You're changing the facts. In my example I merely own a pile of dollar bills. On those facts I get screwed. Perhaps in the interests of the greater good of society, but personally screwed nevertheless. That's the real transition problem you need to face. I suppose, but seriously, who just sits on piles of bills? The money is usually invested in some way, shape or form, with any gains on that investment currently subject to tax. Without an income tax, you would have an increased buying power with the same investment because you would get all of it -- no cutting the IRS in on a share -- when you cash in on it.
I suppose someone who just stuffs money in their mattress won't get those benefits, but even still, they are not hurt by the plan.
Unfortunately, you're just wrong. My dollar bills get taxed when earned and again when spent. Your dollar bills get taxed only when spent. No way is that fair.
I'm using the dollar bill example to illustrate the principle as clearly as possible. Complicating it just confuses the analysis.