The premise is will kids quit/skip a high school team to run club. I am going to assume you mean quit/skip a public school (which should be more correctly called a government school, for that is what it is).
The answer is yes and no. And I can't cover all the reasons, but here are a few I think will suffice.
Yes, if the athlete realizes that the school team/calendar/coach aren't quite up to par to help him/her get to the next level (maybe earn scholarship, be a champion level athlete, etc.) Yes, if he/she realizes that the local public school system offers no real support to their individual goals. Yes, if his/her parents have the money and can make the sacrifices to join a really good club/elite type environment suited to helping them get to their goals. So, 'yes', if the athlete is more of a type-A personality who wants the competition, understands that to be fast you have to mix it up with people faster, realizes they have to take the initiative to craft their own 'running' destiny. Yes, if he/she is capable at an early age of having a more long-term vision of running and where it might take them, or at the least help make him/her into a better person (the discipline gained from buckling down and working at something for several years can translate into other areas of life). Yes, because the point no one makes in these types of posts is that public schools are epically failing kids in America...they were never designed to produce functional, independent thinking, disciplined citizens...they were designed as a job welfare program to produce factory/industry workers who had basic reading/math skills to work in the factories/businesses of corporate America and make enough money to buy the products that they themselves made...I know...sounds conspiratorial, but anyone who is willing to go down the rabbit hole will realize that most of the big money that was dropped into getting compulsory 'education' in American starting in the late 19th century (and where it came from) will realize they )(people involved: politicians/corporatists/bankers) were basically trying to make a permanent dependent serfdom out of America. And that carries beyond the classrooms onto the athletic fields as well. But public/government schools are dying (they never realized how technology would so quickly replace/outdate them). So a lot of states are offering 'choice' and 'vouchers' (tax credits basically) to give parents/families options...and the more those are offered you will see more and more kids exiting public/government schools...so keep that in mind as an answer to your question. More kids exit, then there are less kids to do sports in that area. Basic demographic shift.
No, if the athlete can't think outside of the public school system or isn't exposed to a better culture/environment/context that illuminates that the school team isn't really all that good (or has those 'bad' coaches that don't care, don't know how to develop, etc.). No, if they are more of a social athlete, a human being that enjoys the company/fellowship of a team environment. No, if they are an athlete that would rather be a big fish in a small local pond. No, if running (or any sport) is less important that academics, building a 'resume', etc. No, for a lot of young people because they become more aware of the opposite sex/gender and lose all interest in sports. No, if the high school team/coach/culture is decent enough for them that they can supplement on their own to add to training. they might not be getting.
These aren't all the reasons, maybe not even the 'big' ones, but they'll do for now. As a disclaimer, I have never coached at a government school or a club system.