Soldier is great for dishing out tons of damage, but he doesn't secure kills. Think back to how many times you've shot up a Roadhog only for him to run around a corner, get healed to full and come back. Every single time you do that you're not actually contributing to your team, you are contributing to theirs as good Ana players will charge 30-40% ult out of your meaningless damage dealt.

This applies to team fights as well. If a Genji whips out a sword and starts going to town on your supports, YOU NEED to kill him or you will lose, but Soldier requires so many bullets to hit that if you don't have ulti, you're almost always going to die.

You can obviously aim, otherwise you wouldn't be so high up on the stats, but the unfortunate reality is that Soldier is just not a very good hero. He's damage comes in slowly, is easy to outheal, and he loses the majority of the duels once other DPS heroes get in his face - all things that can easily change the course of a fight in the opponent's favor.