I grant you that the papacy became stronger under the guidance of the Holy Ghost over the years, and certainly the Church remains conciliar even today, but where do you find “the absence of any clergy that manage the relationship between the believers and God” in the scripture?
I'm sure you would.
I think history bears me out on this, the opposite is what has occurred. Instead of being throughly directed by the Holy Spirit the RCC has become man centered with a whole host of doctrines/dogmas that are not Scriptural. The RCC has recreated the Judaic model with a stratified clergy that rules the laity. In the RC system it is the clergy that mediate between GOD and man, dispensing Grace as they see fit.
Our Saviour Jesus Christ did not set up this model. Instead what he told us is so simple we have a need to make it complicated.
John 3:16 For God so loved the world that he gave His only begotten Son, that whoever believes in Him should not perish but have everlasting life.
ITim. 2:5 For there is one God and one Mediator between God and men, the Man Christ Jesus,
The monobishophoric system that developed after the Apostolic Era was never of new covenant design. I have no doubt that many of those responsible thought they were doing a good thing, but the end result has been a neutering of the gift of the Holy Spirit.