In Islamic belief, there came many Messengers before Muhammad. For example, after Abraham, Moses was sent.
Why did God send Moses after Abraham? Was not teaching of Abraham good enough? He taught oneness of God, did He not?
What happened that God decided not to send another Revelation, a Messenger with a Holy Book, after Quran?
What did happen specifically after Muhammad, that there are no more Messengers required?
I am more interested to know the logic behind this from a muslim point of view, supported by verses of Quran and hadithes.
Salam
Messengers come in groups known as "The House" "The people of the House" "The family of the reminder" of that time.
The Quran talks about the last day, so the world is coming to an end. If the world is coming to an end, there will be no matter what a final Messenger.
Mohammad is not the final Messenger, he is the Final Nabi, which means recipient of a revelation to be revealed to humanity. The final revelation to humanity is Quran. The Final Messenger is the Mahdi.
Another way to phrase your question is to say, "How do we know Mohammad is the final Prophet and the Mahdi the final Messenger?"
To do that we must look at God's plan. The plan of God seemed with every founding Prophet, was that he was sent to his people and particularly, they were all "ummi" in the sense, they were raised and born in the central town of the towns they must warn. But God's plan was never with any Prophet, to make their religion forever and their teachings and authority, just local, and not spread.
It was supposed to be the people who receive the message that then help the succeeding Messengers (Awsiya/Successors to the founders) spread it to all humans.
A Prophet that is a not a Messenger is rare case, where a revelation is revealed without need of the message being emphasized either therein or clarified by that Prophet to people. A Messenger that is not a Prophet is rare case, and is the case of the 12 Imams, where they are entrusted to convey the clear message and revive the religion, but without a revelation from God.
Aside from this, Messengers weren't always present, but Guides always were. That is to say during time of Jesus to Mohammad, there was no Messenger from God, but there was a Guide and a witness, and that was a former Prophet and Messenger, Elyas.
There is always a Guide.
Not only that, but there is always a period of darkness from God manifesting miracles and clarifying the truth, these are known as to be "nights" and there is always periods where God did manifest through miracles and there is always a Guide that can manifest miracle be he hidden or manifest, but when the miracles are in the open and the truth is clear, it's known as "day".
God always rotates between these two cycles, because if he kept it with clear miracles all the time, people would be destroyed as they would have no rest from the truth and if they were in oppressive unjust state, they would be met with destruction like many destroyed nations and cities of the past.
When God appointed the successors of Mohammad, there was hostility, and to avoid catastrophe that is surely cannot be avoided if God determines it, he out of his wisdom, hid the final successor to Mohammad.
The Mahdi is yet to be a Messenger, but while, he is not that, he is not useless, but like the Cave, Khidr, Thal-Qarnain in Suratal Kahf, he is a hidden guide and acts and helps in mysterious ways. Aside from that, God only guides at the end through his guidance, and for every people there is a guide. While in the past, we can just go meet him and people took advantage of that with hostility towards the Guides and their followers, all to prevent God's Rule and Kingdom, we can ask God to make us meet him and we can ask when we meet him for God to allow to show us miracles. The Quran shows whether manifest or hidden, there always a Guide to show miracles and make us certain.
When he comes with the final Message, one of the plans, is that he has the Quran with the commentary of Ali. Imam Ali (as) kept track of where every verse is revealed. Today this can be put into a program (the dates of every verse), and we can even see a long with Ali's commentary, how the Quran was dynamically built.
Indeed the Quran was dynamically built, and it was not just for a temporary reason, but the Mahdi will make use of this commentary and reveal the true wonderous clear Quran that dark forces try to make ambiguous and hide it's bright proofs.
The sorcery is what makes Quran confusing to many otherwise it's a very clear book.
This plan, to make it not that the 12 Captains succeeding the founder to the ship of salvation, to be Anbiya, is so that the Quran is not disputed. It's not the case, that we have other claims of revelations from the 12 Imams which Muslims will say is not Quran even if they were on par and from God.
Another reason to seal revelations and protect the Quran this time, is because most of the battle for truth; lied in authority and interpretation. Even during the time of Anbiya of children of Israel - people relied on authorities not appointed by God to understand the teaching of Moses, and this is while God was revealing revelations, and they would rely on these so called scholars to know if a Prophet is true. As a result, they for example, denied Jesus over a trivial thing, that he had no father, and said you can't be linked to David on that. This is what despite his miracles and the high nature of the Gospels revealed.
The Quran is such that it became that it's not longer a big battle upon what revelation is from God - and what is corrupted and what is not, but it's on interpretation. The Mahdi thus is a plan for God - to be regarding manifesting the true interpretation of Quran and other holy books.
The Quran command us to seek the family of the reminder for knowledge of the religion and to seek interpretation from God's rope, and to use the Quran to dispel it's own ambiguities true, but also with the help of ahadiths and also with the help of the current guide of our time.
The family of Mohammad's authority is yet to be replaced brother and the battle for interpretation of Quran is not over.