Don't get me wrong, bro. i'm not trying to prove shiism is right or otherwise. From what little reading i've done, all i'm saying is that they have ground for their belief.
This isn't about the appointment of the twelfth Imam, we accept his appointment (for argument's sake) and we pledged allegiance to him ( for argument's sake), the question is when it is necessary for him to leave, why doesn't he appoint someone to take care of the affairs of the Ummah like the Prophet (ﷺ) when he left for Tabuk and let Ali be in charge of Medina. So trying to prove the Imamate of the twelfth has no application here, it is not what is in question.
[i think your premise is not quite right. One way of reading it is: The Prophet saw left Ali in Medinah to let the ummah knows Ali is the leader after him saw. the 12th imam has no need to do this since there will be no successor for him].
Anyway....the detail is:
the 12th imam is the last in line; there will be no successor for him. with regards to not being physically accessible to mankind, you can read up the article
the necessity for the existence of Imam Mahdi. the article will answer
The opponents of Shi’a protest that although Shi’a consider the Imam necessary in order to expound the injunctions and verities of religion and to guide the people, the occultation of the Imam is the negation of this very purpose, for an Imam in occultation who cannot be reached by mankind cannot be in any way beneficial or effective. The opponents argue that if God wills to bring forth an Imam to reform mankind, He is able to create him at the necessary moment and does not need to create him thousands of years earlier.
With regards to the Prophet saw, this is what i know so far.
Some believe, caliphate succeeded the Prophet saw.
Some believe, imamate succeeded the Prophet saw.
This happened some 1400 years ago.
Today, a newly converted muslim has 2 options.
1. Ignore/forget all the differences that have occurred through out the history and concentrate on doing good deeds as prescribed by
[Shakir 5:48] And We have revealed to you the Book with the truth, verifying what is before it of the Book and a guardian over it, therefore judge between them by what Allah has revealed, and do not follow their low desires (to turn away) from the truth that has come to you; for every one of you did We appoint a law and a way,
and if Allah had pleased He would have made you (all) a single people, but that He might try you in what He gave you, therefore strive with one another to hasten to virtuous deeds; to Allah is your return, of all (of you), so He will let you know that in which you differed; 2. If he/she feels otherwise, then investigate without prejudice, what is the truth.
Under option 2, the pertinent question to ask: Is a Prophet, first and foremost, a ruler of a kingdom or a representative of Allah.
If the primary function of a prophet is kingship then anyone holding the reins of power after him, is his rightful successor.
If the primary function of a prophet is as a representative of Allah, then his rightful successor must also be a representative of Allah. This representation can never be bestowed upon anyone by his people; it must come from Allah Himself. In short, if a successor is to represent Allah, he must be appointed by Allah.
Allahu a'lam.