What does Willa Cather suggest is necessary to enable human beings to deal more adequately than Paul does with the fears of human existence in "Paul's Case"?
The line that summarizes Paul's character in its entirety is when Cather says:
Perhaps it was because, in Paul's world, the natural nearly always wore the guise of ugliness, that a certain element of artificiality seemed to him necessary in beauty.
This means that Paul's nature is to find flaw in the regular aspects of life. He has a specific, and unique, nature that seeks for the ultimate aesthetic expression while bypassing the natural, and predictable. However, Paul's real fear is not of human existence itself, but the fact that the his own existence does not meet the extremely high standards that he wishes for himself.
Being a middle-class young man from a good family, in Paul's eyes, is to be mediocre; it is to be "everyone else", while he desperately seeks to be a part of a much more vibrant, exclusive and sophisticated society. It is not much the money, but the lifestyle that money brings with it what Paul yearns for the most.
Therefore, in order to deal more adequately with this fear, Cather presents us with the characters of Cordelia street: "the girls" that make the lemonade, the "young man" who is clerk to a magnate...all of the rudimentary "types" that Paul so desperately wants to run away from. Therefore, it may be that Cather suggests realistic thinking, understanding, and thankfulness as qualities that one must possess in order to accept life the way it has been given to us.
Nobody picks the place where they will be born and raised, so if Paul had learned to be a bit more appreciative of what he does have rather than dream forever about what he does not have he would have been much happier.
I don't necessarily agree with your question, I am afraid. I think if we read this excellent story carefully, it becomes clear that Paul's problem isn't so much the fears of human existence as the fear of the wrong kind of human existence for him. What Paul cannot stand is the reality of life as a middle-class individual. He definitely can tolerate life, and indeed flourish, as an upper-class socialite, as he manages to achieve at the end of the story when he runs away. Note how he thinks of his home, however:
The nearer he approached his house, the more absolutely unequal Paul felt to the sight of it all: his ugly sleeping chamber; the cold bathroom with the grimy zinc tub, the cracked mirror, the dripping spigots; his father, at the top of the stairs, his hairy legs sticking out from his nightshirt, his feet thrust into carpet slippers.
What Paul cannot tolerate is the kind of life that his reality consists in. His fantasy and love of art and illusion has no room for the reality of life. Paul's problem therefore is not that he fears human existence as such, but that he is unable to keep the boundary lines between art and life in place in order to allow him to live a normal life where he can accept reality.