Precisely why I chose it. It's about as good as a fighter can do at displaying superior skill, /because he's a fighter/.Bounded accuracy does prevent breaking away from the d20, but an archer fighter might not have been the best example. Fighters can sneak bonuses into that type of contest. Against an unmodified d20 that caps out a +14.
Damage and Extra Attacks don't show up in any sort of formal contest, but Archery Style's +2 is relevant to hitting that ittybitty target downrange.
(Though I would skip feats, as their optional, we're spotting the fighter a 20 DEX and 20 levels vs 10 DEX an no proficiency, that speaks to having put ASIs to that stat. So, I mean, seriously. It should be an absolute route from the get-go, in concept.)
I'd also rather just leave Adv/Dis out of it - it's a fair contest, no one's at a disadvantage. (Or, hey, everyone is given time to aim carefully in a safe environment - automatic advantage for all - and also under the stress of competition, for automatic disadvantage. There, gone. ;P )
Depending on the structure of the archery contest, you might be guaranteed to place well, or you might drop out in the early rounds. For instance, if it's single elimination of pairs - whoever gets closest to the bullseye moves on. The fighter only needs to roll really bad - under 6, while the other guy rolls really well, and he's out. If he overwhelmed the d20, he'd stride through the ordinary competitors without effort, splitting the arrow of anyone who rolled a 20 like Robin Hood, but, at "only" +14, he's subject to one bad roll undoing him.
Now, if it's a methodical contest on points, where everyone fires 100 arrows and totes up points for which band they hit on the target, the fighter wins handily. But I don't recall Robin ever winning on points.