How can we improve upon
Bitcoin's highly concentrated coin distribution?
Only the top 3% should be power-law concentrated, the rest distributed with diffuse gas random concentrations:
"Exponential and power-law probability distributions of wealth and income in the United Kingdom and the United States" by A. A. Dragulescu and V. M. Yakovenko
Bitcoin will spontaneously be distributed according to the same laws as other forms of wealth, ceteris paribus (ie. "given that the other parameters stay the same"). It takes some time to find the
dynamic equilibrium, after which the situation looks static from a
statistical point of view.
We shouldn't give coins away to the lazy who do nothing to earn them, because Risto explained that in Russia the recipients just squandered the gifts.
Value cannot be created by fiat. In a way or another, you have to sacrifice something to attain something valuable. The community that put 1000s of hours into Bitcoin software development, mining and forum in 2009-early 2010 did it in anticipation of a reward. Bitcoin was
the most undervalued in its history in 6/2010, when it could still be purchased at $0.005 in OTC trade. Only then started they receive a reward for their investment. Mining coins was a useless waste of time and talent if the coins had no value.
In your proposed system, the coins would be distributed so widely that you would not attract the best and the brightest to participate in the beginning. Great expense of time would be invested, to get $20 per year in "free" coin rewards. Such a system attracts peasants, not kings. I have declined much greater offers of "free money" and so do most of my friends, all the time. We don't have the time to pick all free money that is available. I even waited for Bitcoin to prove itself by going up 100x and down -90% before investing.
I can already buy anything I want from peasants with my bitcoins, gold, silver, euros, dollars, and (new!) rmb. You are creating a 3rd world currency with noble aims but I highly doubt that it will ever fly, since it does not have a skeleton, which is required to direct the energy to the wings. Bitcoin has its skeleton (a community, early adopters, power law) firmly in place. Ripple is an example of how not to do it.
By trying to annul power law, you mutilate your creation so that it cannot function.