Jesus had the perfect opportunity to state, or at least foreshadow, that Rome would play a role in Christian worship. As soon as she realized Jesus was a prophet, the woman at the well explicitly asked him about the proper location to worship. Jesus’ answer clearly indicates that physical location is no longer a factor:
John 4:
21 “Woman,” Jesus replied, “believe me, a time is coming when you will worship the Father neither on this mountain nor in Jerusalem.
22 You Samaritans worship what you do not know; we worship what we do know, for salvation is from the Jews.
23 Yet a time is coming and has now come when the true worshipers will worship the Father in the Spirit and in truth, for they are the kind of worshipers the Father seeks.
24 God is spirit, and his worshipers must worship in the Spirit and in truth.”
I wasn’t talking about Rome’s role in Christian worship, which is a new topic you’re introducing. But John 4 (which I just taught a Bible study on last week) doesn’t say “physical location is no longer a factor”—what Jesus does say there about physical locations simply indicates the center of worship will no longer be on Mt. Gezirim (the Samartian center of worship under discussion) or Mt. Zion—though it’s correct that Jesus places a greater emphasis on the spiritual worship there, foreshadowing the coming of the Holy Spirit and the fact that Christians are temples of the Holy Spirit. But as for the role Rome would play in Christian worship, Jesus does allude to it in his prophecy about the destruction of the Jerusalem temple (building on Daniel’s discussion of the fourth beast which also referenced Rome being conquered by the Messiah), and there is also an emphasis on Paul’s progress towards Rome in Acts, in addition to the references to Rome in Revelation; plus we have the witness of the 1st-century Roman bishop Clement of Rome and of Ireaneus, among others.