What you are doing in your lengthy theory is using the rejection of some true historical Biblical truths to justify a perpetuated tradition (you likely also support NT ministers distinctively titled priests) that was reject by churches which held to historical Biblical truths.
The SBC affirms the latter but rejects infant baptism, as paedobaptism is not what Scripture most plainly teaches but was a tradition which developed at time went on. Again, unlike circumcision, the Biblical requirements for baptism require repentance and faith, and which infant are incapable of.
Nor does the act of baptism make one a believer unless one can believe. God has no grandchildren as no one is saved by proxy. Period.
I’m not a Roman Catholic, I’m reformed. Believer baptism is not the plain teaching of scripture. It’s hardly a surprise that we see adults who were already part of the old covenant via circumcision getting baptized into the new covenant as believers. Abraham was a believer when he was circumcised. Both circumcision and baptism are signs and seals of God’s covenant, it would be absurd to include children in the old covenant but reject them in the new.