If any physical location was to factor into Christian worship, Jesus would have said so. He didn’t play games or get cute with people. When He was asked a sincere question, Jesus gave an honest answer.
The Samaritan woman asked Jesus where worship should be centered, physically speaking. His answer was to contrast physical location with the new standard. The new standard is not a location, but a state of the heart. I.e.: from now on, true worship is that which takes place in spirit and truth.
There is no honest way to get Rome from Jesus’ answer. Were Rome to be in any way significant, an honest person would have said so. Jesus didn’t force us to play guessing games. He said what He meant, and He was always honest.
From that time onward, true worshippers were/are those who worship in spirit and truth. Heaven help us if we add more to this teaching than Jesus saw fit to add Himself.
Jesus did contrast physical-centered worship with spiritual-centered worship in the chapter we're discussing, but he did not go on to state, "Therefore, Rome isn't important for the plan of salvation." He was specifically addressing a dispute between the Samaritans and Jews about where the proper center of physical worship was, and if you notice, he sided with the Jews in recognizing the importance of Mount Zion over Mount Gezirim ("we worship what we do know, for salvation is from the Jews"), so he did not teach physical location was irrelevant under the old dispensation. Nor did he say it was irrelevant under the new dispensation. What he said was, "God is spirit, and his worshippers must worship in spirit and in truth." He did not say that this meant his worshippers should disregard the role physical location played in the plan of salvation. What he was getting at becomes more apparent later in John when he talks about sending the Holy Spirit and about "other sheep that are not of this sheep pen", i.e., the evangelization of the Gentiles and the pouring out of the Holy Spirit on the Gentiles. Rome became the epicenter of the evangelization of the Gentiles, which is one of the themes of Acts and Revelation and is alluded to other books.