the total number of coins would not be limited and it will rise over time.
I won't use that system, then.
I don't see how wasting electric energy for useless calculations that do not benefit the society called work.
We could also decide that each hundred jumps in the air will get a coin.
At least it could be something useful like starting global projects
I don't think "global projects" are useful.
The thing about useful is that it's a subjective opinion, not an objective fact.
(Hint: the calculations that block-generating bitcoin nodes perform are not there just to waste time, though you might have read otherwise.)
I'm saying the decided method on how the total sum of coins is distributed is not fair, and the only fair method is to distribute it equally.
Distributed at what point in time?