TLDR: Scout's abilities make it appear more successful than it is, and the majority of Scout's successes come from the coordination and ability of the soldier/demo/medic of the scout's team.
Personally I believe that Scout is often referred to as the dominant class because scout in the current meta plays well off of the work of other teammates. Certainly the scout is very good in 1v1s but to be completely honest, this game does not always rely on 1v1s, and that is kind of a good thing. In the big team fights, even though scout does not do splash damage, scout is still versatile and viable because of the ability of scouts to "clean-up" on the damage output of soldiers and demos. I think it seems almost unfair to base whether or not scout is balanced on the ability of these damage output classes to last against a scout in every 1v1 situation.
Another important aspect is the "bombing" or "sacking" of soldiers into the combo. Yes scouts are great at denying a bomb from a soldier but I almost feel like that is the point. If a soldier was able to bomb effectively every time it would almost make it too difficult for a team to ever hold aggressively and would just encourage the meta to rely solely on a push from the offensive team, which isn't the best imo, I would rather see either team with the ability to push.
I actually would be interested in seeing the effects of slightly nerfing the damage spread of scouts at mid to long range, but again I do not think it will or should make much difference. I think the current meta does a great job at glorifying scouts but that comes from people looking at logs or at clips of frag videos and forgetting that soldiers and demos play a big role in laying down damage and securing chokes/winning big fights.
I do not think there is anything wrong with scout inherently winning 1v1s against other classes. I like the idea of a balanced meta/game not every aspect being balanced. Besides, scouts can just be more fluid if you really want to avoid a 1v1 scout v soldier to help out your soldier tbh.