Value in olympiads

More so, is there any value in just qualifying for olympiads, like math olympiads, even if you don’t get any distinction from them?

Sure. For instance, qualifying for USAMO is a big deal in math. Not a guarantee of anything of course, but it’s one of the premier accomplishments for a high school STEM student, especially because in any given admissions year there are only going to be about 200-250 qualifiers in the entire applicant pool.