You are working hard to to utterly absolve Rome from condemning souls to Hell, but the fact is she does in the judgmental sense, judging them as damned (for those who die in mortal sin), as we also do by preaching the necessity of salvation and surety of damnation to those who deny Christ, even if we do not have the actual power to put them there.
So much more if Rome claims the power to bind men in their sins. The Supreme Court also does not have the power to enforce what it decrees, but if it judges a man guilty of a capital crime, then what it decides effects enforcement by the entity that has the power and that awaits its decree.
And again in the judgmental sense, “By faith Noah, being warned of God of things not seen as yet, moved with fear, prepared an ark to the saving of his house; by the which he condemned the world, and became heir of the righteousness which is by faith. “ (Hebrews 11:7)
“The men of Nineve shall rise up in the judgment with this generation, and shall condemn it: for they repented at the preaching of Jonas; and, behold, a greater than Jonas is here. “ (Luke 11:32)
The priest who refuses to remit someone's sins does in effect, condemn them to hell. Just because they leave God to do the dirty work, if they really believe that the the Church has the power to bind a man's sins to him or remit them, then they are the ones who are making the executive decision. That makes them responsible.
Rome is a city and I have no power to absolve a city. But you are working hard to utterly condemn the Catholic Church. Best of luck with that.