I knew a classmate who openly admitted to putting made up volunteer activities on her college applications, arguing there was no chance the school would fact check her. She was right!
The problem with these is that they couldn't have been significant enough to make a dent in the outcome. Pretty much all significant achievements are fact-checkable. E.g. you may falsely claim that you were doing karate or basketball, but if you did win any trophies, then most selective schools wouldn't care about you.
You might be surprised. I was on the committee which adjudicated major entrance scholarships for six years, and I can count on my fingers the number of times someone said "can we get some verification of this?" We've never thought that fraud was a common problem, and when you're competing to recruit the top students you really don't want to go back to them and accuse them of dishonesty..
And (although we're revising the system and hopefully changing this part) the relative weighting of "significant achievements" of an easily fact-checked nature vs. "doing lots of stuff" has skewed heavily towards the latter; you could have a resume full of "volunteered at X" and "leader of student club Y" which would be worth as much as the difference between a 90% high school average and a 95% high school average, while containing nothing which would show up online or elicit commentary from a referee beyond "this student is heavily involved".
(We're putting together a new system starting next year which is aimed to be more about identifying students who are in some way exceptional as opposed to merely being generally all-round good people. A large part of the motivation for this is to avoid easily "gamed" metrics; nobody spends 15 years playing violin or becomes a national chess master simply because it will look good on their resume. So with luck we'll end up having less of a fact-checking problem in the future; but we're still going to have a significant amount of trust built into the system.)
A few years ago, I was mentoring at the local (major!) university and met a student who was the President of a club. Then a week later, met another student who was the President of the same club. A few weeks later, the same.
It turns out, a bunch of students got together, created a club, and each member was called a "President." The best part is that if an employer ever checked, any member could honestly say "yes, he's a President in that club."
I never really understood why admissions committees give any credit whatsoever to 'well-rounded' students. If somebody spent all their time volunteering in 10 different inconsequential clubs, playing 5 musical instruments, and participating in 3 different sports, I would consider them a 'tourist' or a dabbler, if you will, and wouldn't give them any credit. Now if they happened to win a championship, get a gold medal, or qualify for the Olympics, etc., then that's an entirely different story.
You're pretty much preaching to the choir here; but the position I hear most often is that when we're selecting the students we want to have as part of the university community, we should pick students who will contribute something to said community (beyond "mere" academics).
In some cases, I see students' extracurricular activities as demonstrating an ability to dedicate themselves to a cause or pursuit; that sort of perseverance is important in higher education. But in most cases that sort of dedication goes along with extraordinary success of the sorts you mention. (My personal scholarship assessment rubric actually includes a specific value for "competed in the Olympics or equivalent level of international competition".)
What's wrong with doing a bunch of stuff instead of being the best? These kids are in high school, maybe they just wanna try out a bunch of clubs and see what interests them in college and beyond.
" nobody spends 15 years playing violin or becomes a national chess master simply because it will look good on their resume."
I don't understand why is doing doing extracurricular in order to get to good university seen as "gaming". If anything, it is quite responsible behavior.
Due to the volume of applicants and the rise in competitiveness, don't you end up being faced with a glut of exceptional candidates anyway? In which case the selection would still inevitably amount to a draw based on arbitrary criteria or simply the way committee members felt that day.