Islam is pretty normal in being similar to post Christ religions, all claim to be a new and final revelation or prophecy. Bahai uses the same verses and concepts as Islam claiming Bahai was a new and final prophet. This is true of Pentecostals, Mormons, and even Catholics. All claimed new revelations after the New Testament of Jesus. Some couch prophecy under the term mysteries revealed or later understandings. Each eastern religion has the same problem. Jesus said his Testament was final and complete. Finished through the Holy Spirit's guidance. Jesus also taught the immediacy of the Kingdom, it would not be put off for hundreds of years or generations. The messianic Kingdom was immediate. It was God's kingdom and not worldly as Satan offered Jesus in the temptation.
Matthew 4:8
Again, the devil taketh him up into an exceeding high mountain, and sheweth him all the kingdoms of the world, and the glory of them;
Matthew 4:17
From that time Jesus began to preach, and to say, Repent: for the kingdom of heaven is at hand.
The implication of this immediacy is a death blow to all future prophets like in Islam or Bahai. Prophets 700 or 1500 years later can't fit into the immediate kingdom concept.
Jesus in Matthew 4 turned down all worldly kingdoms for the Kingdom of God. Islam and all future prophets tend to focus on this world's power. They want to dominate this world, but they can never control the Messianic kingdom. Peter proclaimed in Acts 2 that Jesus was seated and governing. Acts 2:20-26.
Acts 2:36
Therefore let all the house of Israel know assuredly, that God hath made that same Jesus, whom ye have crucified, both Lord and Christ.
Within these passages Jesus is granted use of the Holy Spirit is ordering his kingdom and gave the gift to the early church to order the messiah's heavenly kingdom.
John 14:26
But the Comforter, [which is] the Holy Ghost, whom the Father will send in my name, he shall teach you all things, and bring all things to your remembrance, whatsoever I have said unto you.
You see Jesus promised an immediate and complete revelation to the Apostles and the early church. This was fulfilled in the generation of the Apostles. All false religions must put this off for hundreds or thousands of years. It was a promise to the Apostles and 1st century church. Notice the verses confirming it immediate completion in that generation. The early church had everything needed for eternal life and godliness.
2 Peter 1:3
According as his divine power hath given unto us all things that [pertain] unto life and godliness, through the knowledge of him that hath called us to glory and virtue:
No future revelation was needed for these things, they did need to dwell upon what was already given to them. The promises were eternal. Notice all future prophets claim, basically lie, that their prophecy adds to and completes Christ, they say Christ wasn't complete and final. Yet, our inheritance doesn't fade away according to Peter, it is stable forever. It is finished. Once delivered.
1 Peter 1:4
To an inheritance incorruptible, and undefiled, and that fadeth not away, reserved in heaven for you,
Jude 1:3
Beloved, when I gave all diligence to write unto you of the common salvation, it was needful for me to write unto you, and exhort [you] that ye should earnestly contend for the faith which was once delivered unto the saints.
All future prophets have to deny these passages. the faith reserved in heaven and eternal. There are other passages that confirm what I am writing. Consider
I Corinthians 13.
1 Corinthians 13:8
Charity never faileth: but whether [there be] prophecies, they shall fail; whether [there be] tongues, they shall cease; whether [there be] knowledge, it shall vanish away.
1 Corinthians 13:10
But when that which is perfect is come, then that which is in part shall be done away.
The word perfect hers can be translated "complete", some believe it is the complete revelation of Jesus Christ. At the time this was written there were other epistles and revelations to be completed. The completed revelation was future. It is talking about an immediate cessation of prophecy shortly.
This can be confirmed from Daniel 2:44.
"Shall not be left to another people"
The messianic kingdom was only for Christ's church, not Islam.