There is not such thing as fair distribution...
No one should get something very valuable for free as most probably won't appreciate it, sell it and get the free money that someone gave to you...
The most fair distribution would be to create something very very simple that anyone outside crypto who can at least send an email can participate. As long as only existing cryptoinvestors participate and not the rest of the world it will never be fair.
You said there is no such thing as a fair distribution and I completely agree. Then you say no one should get something very valuable for free because most people wouldn't appreciate it etc and to a certain extent I agree.
However...
Bitcoin early adopters got rich for free if they were smart enough not to quickly sell it. They mined thousands of coins with their CPUs and saved them. Satoshi Nakamoto himself did this and we say this is perfectly fair distribution because everyone else had an equal opportunity to do the same thing among the people who knew about Bitcoin.
The problem today is people know about Bitcoin but cannot mine it. It's now Pay-to-Win. It was not Pay-to-Win for the players who played in 2009, 2010, 2011, until GPUs came out and changed the game.
This is not the game Satoshi Nakamoto described when he said one CPU one vote. A vote could also be an opportunity. So one CPU one opportunity. It doesn't mean everyone will win but at least if you have a CPU you have some stake, some chance at achieving a stake, but today a CPU is worthless.
I do agree with you that only people truly interested should get the biggest rewards. Interest should be rewarded but not previous wealth. If you reward wealth then people who have no interested in the technology, the community, can just buy us all out.
Diversity of playing styles, strategies, and game types should be encouraged I will say that different sorts of games provide different advantages to different demographics of players. This is okay just so long as we keep switching the games up so the same demographic of players don't receive all the advantage all the time. Allow room for skill in the game but don't make it a skill which an exclusive small segment of the nerd population has and then expect that the rest of the people will come running for a seat at the table because to them it's like the poker champions playing while card counting.
I believe if we could devise a series of fun but serious games, that allow the players to exert a reasonable amount of effort to try and win, or gain an advantage by having a unique playing strategy, then if they win more shares it was fun to do it and required strategic thinking.
https://en.wikipedia.org/wiki/Advantage_gambling