You get ten points like this:
(x+20)/2=10, where x is an infinitesimally small value based on the first (non-linear) calculation method. Am I understanding your idea correctly? So, the point is that after he gets 10 points, they will be "increased" to 20, according to your suggestion. That is, all participants at the end of the long list will receive 20 points, regardless of how they performed...
Note: we can abandon this idea.
I will rework the second formula so that all points start from zero, not from 20... There are no problems. It's all feasible. I just consciously want to introduce a minimum threshold "for participation"... That's the idea. If it doesn't work, then the formula will take on a strict form according to your comments, i.e., the last place in your exaggerated version will receive (0.1+0)/2=0.05 rating points. And then no one will want to participate in tournaments anymore... :)
On the contrary, in the VDV tournaments, I try to separate the rating, which shows the current skill level. VDV gives everyone grails for oil and descriptions and for everything else, so there are no particularly upset players yet.