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.
Rassah. Let's consider your argument seriously. It has some valid points.
You are arguing that PoS transfers additional wealth to savers. It is actually a sound argument. Saving in PoW requires a conscious decision to reinvest mining proceeds. Saving in PoS occurs by default. A wide body of research suggests that setting up default choices for people influences their behavior. See the pop-economics book "Nudge."
Your argument also has some serious weaknesses. Look at the quotation in my signature line, "Does it contain any abstract reasoning concerning quantity or number? No. .... Commit it then to the flames: for it can contain nothing but sophistry and illusion." What your argument is missing is some 'reasoning concerning quantity or number'. In particular, we don't know if the effect you are describing could be quantitatively important. If fees are near-zero, the money given to stakeholders will also be near zero. Thus, the quantitative significance of this phenomenon could be negligible. If so, we can safely ignore the argument.
To make things more concrete let's discuss the phenomenon in terms of PPCoin, the only operational PoS system. PPCoin awards 1% interest per annum to anyone who saves. This is the PoS award. Since fees are destroyed there is no other way for stakeholders to earn money. How long would it take for a determined saver to double their holdings with this system? 70 years. That is also the minimum possible time for the money supply to double.
I own about 0.2% of PPCoin right now. Let's ignore PoW reward and assume issuance stops today. Let's also pretend that no one else tries to save. I'm the only one. How long will it take me to accumulate 51% from my 0.2% holding? 560 years of waiting. Suppose that everyone else also tries to save. Well, then I never acquire 51% and am stuck at 0.2% for eternity. So the amount of time necessary for me to wait is between 560 years at minimum and infinity at maximum.
I'm not going to live that long and I don't think cryptocurrency will either. Your concern seems to be irrelevant in practice. It is quite silly to worry about something that takes 560 years minimum to become a potential threat. Even the proposed 560 years is silly. It is based on the premises that: a) 20 generations of my descendants save these holdings and pass them on to the next generation. And simultaneously that b) no one outside my immediate family saves at all for the next 560 years.