The app is a lengthy self presentation. Many sections to consider and master. Of course one should dig deep. But that’s not about how a faculty member structures his/her own bio. You don’t get an admit because you pick a prof whose professional interests mirror your 17 yeal old ideas. Grad school needs that more. That’s where faculty admits you. We’re talking undergrad.
“Show, not tell” doesn’t mean “telling” colleges, “I’m great.” Nor is this hierarchical (Wow, he placed in USAMO, let’s admit him!!!")
And it doesn’t matter if one competiton is considered more pretigious than another. Adcoms at holistic top colleges look at the whole picture. USAxO shows some traits and skills, but the whole is larger than that. And many, many top contenders do not participate, but get their admits on their full merits.