This interpretation fits well within the immediate context as well as the wider context of the rest of the New Testament.
In regard to the immediate context, we note that directly after His statement about binding and loosing, Jesus said: “Again I say to you, that if two of you agree on earth about anything that they may ask, it shall be done for them by My Father who is in heaven” (Matt. 18:19; emphasis added).
There again is the theme of “what you do on earth will be supported in heaven.” We on earth are authorized and responsible to pray. When we do, heaven will respond. Jesus’ words, “Again I say…” seem to indicate He is expanding upon His prior statement about binding and loosing.
Jesus’ final statement in this passage, “For where two or three have gathered together in My name, there I am in their midst,” also supports the “heaven will back you up” theme. When believers gather in His name, He who lives in heaven shows up.
Even if you totally disagree with my interpretation of the passages in consideration, you are going to be hard pressed to present a sound, scriptural argument that Jesus was speaking about binding evil spirits over cities!
