Two points, first is that the point of mining is to reveal bitcoins. Where do you propose these mined bitcoins go? Secondly, Bitcoin is an open protocol, there would be nothing to prevent the govt supplying as many of their own ASICs as they wanted.
What I was describing was essentially a Proof-of-Stake system, where the blocks you mine and the fees you collect are themselves an increase in your stake, and thus as if you are mining for more mining equipment. It really is a piece of shit system.