Let's get back on track, the opening post above shows us three prophets who became Imams, three Imams who received revelation.
True, but it also includes his cousin Lut when it follows that by "And Lut", and Ismael. And indeed all Prophets became leaders when they ascended to certainty and the fortitude of being the utmost submission to God which is the full embrace of God's Name and death of all other than him.
Can you show from the Qur'an, that when Ibrahim (as) asked for Imams from his lineage, the Imams in question were other than his actual direct progeny such as his son and grandson the two prophets mentioned clearly by God?
They were from his family, but Qurans shows aside from the chosen families, is the chosen families are all linked back to other chosen families.... and Ismael was pivotal in that regard, and so the reason why God made him born of Hajar first, instead of Sarah who is on par with Abraham, is because he wanted the chosen family of Abraham to be from Jacob (like Yusuf) and the family of Jacob includes Sarah, Ismael, Isaac and Yusuf and whatever Messenger followed that is unamed in Quran, but that it reminds that Abraham was praying that a Messenger would come from Ismael's offspring, and he prayed that a way and course would come from Ismael's offspring down the line, just as Abraham was a way/course to God, as Quran emphasizes on Abraham being a way/course to emphasize what it means by the chosen families include Abraham's being a way or each of them a way from another perspective.
And indeed Moses was expected, and so there was reminder of him, and the succession of Moses was obviously expected, and that Moses was savior and who would found the leaders from the people who were oppressed in the land.
And indeed Mohammad was expected, and so the prayer in this place, is reminding that the True Leaders and Kings, has to come from the offspring of Abraham somehow, but that Ismael going to Becca and living there was for a purpose. That Hajjar didn't suffer due to jealousy of Sarah who is pure and exaled and of the chosen household of blessings of God and his mercy.
Rather it was a plan from God and all these distortions of the purpose of Ismael, God manifests and annuls.
Is there a reason to believe many others from his progeny were also Imams or is prophethood sufficient?
There is good reason to believe there are leaders from God as there is no other holders of authority or vicegerents in reality than the light God appoints us to follow.
Among the good reasons is 4:59. Among the good reasons is many Surahs in Quran which emphasize on the leadership of the family of Abraham to prove the chosen way and leaders who guide by the truth in Bani-Israel, that guide and manifest the Twelve ways after Mohammad, who were but one way and one ship and one door from another perspective.
And among the reasons is because God is not emphasizing their role of leadership to end it, but to continue it although sealing revelations as a mercy and favor to humanity for many reasons of wisdom, which the Quran elaborates on.
And the reason and wisdom of the one who will unite humanity and perfect their intellect through a revelation revealed 14000 years ago is more wise then revealing a revelation in this age. It is a best and most elaborate plan, when refer back to God and the Messenger, this would be the best end and best way, as the Quran is designed with the Ulil-Amr as authorities and religious guidance.
Among the reasons is 5:55. Among the reasons is Suratal Inshirah. There is plenty of reasons. The problem is you are at this point not willing to accept of them including the message of thaqalain and appointment of Ali as Mawla just as Mohammad is Mawla of believers, and Allah (swt) is the Mawla of Mohammad in a way Mohammad is not Mawla of Allah (swt).
Can you show us in the Qur'an, an Imam who was not previously a prophet?
The Quran to my knowledge only manifests the 12 Successors of the Seal Prophets to be not that, everyone else, it has not explicitly stated they are not Prophets. And it makes sense more to me that in the past, as revelation was not sealed to be revealed to humanity, that all leaders would be Prophets and the wisdom of Prophethood would mean God would verify them with revelations as well and they worked with revelations from God.
But the Imams (as) and wisdom of Quran includes putting an end to revelations, and the whole wisdom included something that must be done differently to break the cycle of which revelations were distored and abandoned.
That God is designing a plan that cannot be stopped, that Mohammad's religion would be superior and take over all religions, and that the divisions and hatred would stop eventually on the day of rising of the Qaim.
There is no doubt that oppression happens time and time again and that is upon God through an appointed saviour, to save them, and is upon God to deliver the believers, and has shown the method of past, to analogy of what will take the whole world and an event the whole world must prepare to face or ignore only to their perdition.