The commission of Peter is self-explanatory in his relation to the Church, -- he is given a new name and called the foundation of the Church. It would be extra-scriptural to assume some other meaning in that verse. In Acts, it is rather clear that while others disagree with him, Peter is the one giving the final approval to the doctrine they jointly developed. This is functionally papacy, although the degree of authority the the Pope has among the bishops is matter of debate and interpretation, and it changed through the ages.
When John is named Son of Thunder, there is no particular reason given in the scripture, this is why we don't speculate on any ecclesiastical role of John.
I disagree, as you well know. The RC tradition is self explaintory after you've been an RC and had it explained to you. It may be a bit of reflex to see all of that but scripture alone does not give you a pope at all. Just an ambiguous statement about a rock and another rock. That other rock, the profession not Peter, is the foundation. That interpretation fits with the rest of scripture. The pope explination does not.