If printing money was proportionately as costly as mining BTC, the presses would not stop 'til it costs more than a dollar to print a dollar.
Welcome to the problem of inflation.
It's not like you create value by printing a bill, so you will dillute other peoples value.
It's not like you create value by mining a bitcoin, either. At least the monyz smells nice. And what's wrong with inflation? Who told you it was a *bad* thing?