"paying coins to existing owners is not distribution" ... what an argument ... do you care to explain why this not applies to every coin? - you do realize that almost every miner is not just mining one block, but instead uses his miner to mine for a certain time - which means that he is already an existing owner ...
Sorry, that was not as clear as it should be. I meant not paying to existing "owners", but proportionately to existing
ownership. That is effectively a "stock split" and does not distribute anything. There are other issues with how Dash does it but they are out of the scope of the overall rate of distribution so off topic for this thread.
With mining, it is not in any way proportional to existing ownership. In fact your example demonstrates this as if you continue mining (without selling) your ownership goes up but your rate of mining does not.
so how do you distribute coins in your view?
There are many different ways to do this with various positives and negatives. As long as they are not proportional to ownership, they actually accomplish something, at least.
ok, and not ok

"your ownership goes up but your rate of mining does not." - i do not exactly agree with that ... i guess i see what you want to say with "ownership", so if i mine bitcoin i have bitcoin in my ownership and if i buy new mining hardware, to mine even more bitcoin, i decrease my "ownership", right?
But that seems only like a word play.
In the end the profits from mining are also increasing the hashing power because you could buy new hardware, even if the ownership is going down for the purchase of new hardware it's just a question of time until you got a 100% ROI on the new mining hardware and so in fact your ownership and your mining rate goes up, too !!
What you seem to be skipping here is that competition for cheaper electricity and hardware costs may or may not result in you getting your reinvestment back--AFAIK, Bitcoin has proved that early miners lost that competition to Chinese miners. With a coin like dash that uses a paynode scheme, all you need to do is keep reinvesting and you are guaranteed a greater percent of the stake--unless of course you can attack other node operators to lower the masternode count and increase the ROI%--which gives you the problem of having an inefficient system bent on cannibalizing resources.