OK, the visible head.
Still, a head.
I do understand what a regent is. I just disagree that there is a regent in place, unless you might perhaps say the Holy Spirit is a type of regent, although I’ll tread carefully there.
John 16 -
” 7 Nevertheless I tell you the truth. It is to your advantage that I go away; for if I do not go away, the Helper will not come to you; but if I depart, I will send Him to you. 8 And when He has come, He will convict the world of sin, and of righteousness, and of judgment: “
But not a pope, no.
He did also leave us a church structure; we are to choose out for ourselves elders, also properly translated bishops, and they have authority and can exercise church discipline and so forth. But there is no allowance for a chief or head or ultimate bishop.
You may wish to reread Paul. He had several levels of clergy under his own authority.