You’re overthinking this. The point of Broom Boy is to show how the Force is for everyone and that you don’t need to be mentioned in a prophecy or part of a certain family to use it. And in order to establish this in a quick and subtle way, they showed him grabbing the broom. Showing his enhanced reflexes would require a way longer scene, putting too much emphasis on him. And simply mentioning his abilities in dialogue would be lazy and too on the nose.
Of course I’m overthinking this. I’m a Star Wars nerd!
Seriously though, I actually like the sentiment - that the Force is for everybody (as opposed to genetic a la the PT). But it isn’t free. In the OT (and the PT despite Midichlorians) the Force is a discipline. Luke struggled to levitate his lightsaber in the Wampa cave. He was 23 yrs-old and had been aware of his heritage for the past 3 years. He couldn’t raise his X-wing. Yoda could. This was a clear indication of learning, of slow progress, of mastering his self and his fears and his ego in order to reach for such mastery. I just happen to like that idea. If kids can levitate brooms and Rey can lift a mountain without training then Luke clearly sucked as a Jedi, 'cos apparently this stuff ain’t so difficult!
RJ had already made his point about the Force via Luke’s explanation and Rey’s parentage. We didn’t need Broom Boy. I’d have preferred the film end on the Falcon or have Broom Boy simply holding the Resistance badge and looking to the stars.
Luke was also injured, upside down, (blood rush to the head!) and probably already suffering from the cold.
Broom Boy’s™ broom was not stuck in a pile of snow either.