As a lifelong Protestant I can say that a critical distinction between P and RC is the recognition that human institutions are corrupt. Corruption always emanates from the top down. The institutionalization of the Faith will always be marked by human corruption. Only in a personal relationship with Christ is it possible to overcome evil. No intermediary is equal to the task.
Not a distinction at all. My ancestry is Italian. We saw Borgia popes up close. If we didn't believe that Christ Himself was the real head of the Church and was ultimately going to ensure that the "gates of hell would not prevail against it", we'd despair of the institution faster than any of you.
And by the way, I am a human institution, so I can go corrupt too. And I don't have any Scriptural guarantees to the contrary. You are actually not solving the problem of human corruptibility by replacing the institution with individuals.
However, anyone watching closely in even Evangelical and Pentecostal circles can observe a flesh-driven elevation of religious leaders to positions of not just serving as intermediaries for groveling sheep--but objects of more or less worship by said sheep. Dreadful.
As Claud quite correctly points out, "all human institutions are corrupt" includes the "human institution" you see in the mirror every day. In fact -- and I think you can probably see this in your own lived experience -- Joe Schmoe is probably the least likely person to give a sound judgement WRT his own sins. He's too personally invested in them. (Part of the spiritual reason for the sacrament of marriage, BTW.)
Someone else -- almost anyone else, even someone who is personally a bigger sinner than Joe (as long as he has no personal investment in Joe's sins, which is not true WRT Pope Francis and divorce-and-remarriage, sadly) -- is more likely than Joe to judge Joe with justice.
But I would submit to you that that's not even the question you should ask. The question you should ask is, "What system did Christ himself set up on earth to propagate the Gospel and be a home for Christians?" WWJD, in other words.
If Christ is the perfect God-man, it stands to reason that the system he set up would be, relatively speaking in a fallen world, the perfect system. It also stands to reason that that system would endure until the end of time, because Jesus said as much in the Great Commission.
And only the Catholics and Orthodox even claim to have institutional continuity back to Christ and the Apostles. There are no other possible candidates.