I disagree with your analysis which is easily disproved by the New Testament itself when it illustrates a Divinely-Designed Hierarchy with authority not a democratised free-for-all in which each and every individual has been given authority to decide for his own self what Scripture means.
Rome itself is very deviate from the NT church, regardless of a form of magisterium, while SS does not make the individual the supreme authority, as it uphold the principle of magisterial authority based upon Scriptural substantiation, which is how the church began, not under the premise of obedience to an autocratic infallible magisterium.
And which Rome has infallibly declared she is when speaking according to her infallibly declared *scope and subject-based) formula. Thus all that she enlists for support can only mean what she says it means.
In addition, it is Rome that makes the individual the supreme authority, that being an assuredly infallible pope as supreme over councils, which most Catholics seem to believe he is.