It didn't make it feel like not all trainers were good enough for the League, it made it feel like none of what happened prior to the League happened in a larger world.
Remember that the character we see the most (Ash) is the
extreme exception to the rule. Like him or not, he is in the top percentile of Trainers. The average Trainer isn't even remotely as good as he is.
Ash used to promise to meet the Character of the Day at the Pokemon League. In retrospect, he seems to have been saying
Don't quit and go home! which is exactly what the overwhelming majority of Pokemon Trainers do. It takes a lot of dedication to make it through a region. Even someone experienced like Ash loses sometimes, so it must be horrible for a complete newbie in their first year.
What I'm trying to say is ... the vast majority of badge collecting Pokemon Trainers simply do not make it to the Pokemon League for one reason or another. Of the hundreds of kids who set out the League only has an average showing of less then 200 Trainers. A small percentage of them are League veterans like Ash or Paul who travel from region to region competitively.
It seems that the odds are heavily stacked against you, and yet many of the characters that Ash met this time around managed to make it for some reason. Of all of the League participants I think 1/3 o them were recognized as recurring characters either in-region or in the background from previous seasons. If we did really deep I think the number's closer to 1/2.
I don't know ... it just seems improbable that so many that Ash has met before made it in.