I disagree with that belief. Al Mahdi is not divinely appointed. The hadith which say so are exaggerated and false. We have contrary hadith where people and not some voice will tell the Mahdi to be Calipah. Then the Mahdi will run from that responsibility. He will again be pushed and then after through bayah he will become a Calipah.
Incidentally, I didn't quote the Hadith about the "Voice" declaring the Mahdi is the Caliph of Allah, knowing full well its authenticity is suspect. But I did quote another Hadith which says Allah will بعث "raise" or "send" the Mahdi. The same word has been used for Prophets and Mujaddidin to indicate that they are appointed to their office by Allah and not the public:
فَبَعَثَ اللَّـهُ النَّبِيِّينَ
"Allah sent the Prophets" (Sura 2:213)
Sayyidina Talut عليه السلام was one of the kings whom Allah directly appointed through the agency of Prophet Samuel:
وَقَالَ لَهُمْ نَبِيُّهُمْ إِنَّ اللَّـهَ قَدْ بَعَثَ لَكُمْ طَالُوتَ مَلِكًا
Said to them their Prophet: "Verily, Allah has raised for you Talut as King" (Sura 2:247)
Regarding the Mujaddid being divinely appointed by Allah:
إِنَّ اللَّهَ يَبْعَثُ لِهَذِهِ الأُمَّةِ عَلَى رَأْسِ كُلِّ مِائَةِ سَنَةٍ مَنْ يُجَدِّدُ لَهَا دِينَهَا
"Verily, Allah will raise up for this Umma upon the head of every century one who will renew for it its Religion" (Sunan Abi Dawud #4291)
Now the same verb بَعَثَ has been used, with Allah as the فاعل in the case of the promised Mahdi.
As for your argument that the people themselves will coerce the Mahdi to accept the pledge of allegiance and that the Mahdi will "run from that responsibility" you are basing it on the Hadith:
فَيَأْتِيهِ نَاسٌ مِنْ أَهْلِ مَكَّةَ فَيُخْرِجُونَهُ وَهُوَ كَارِهٌ فَيُبَايِعُونَهُ بَيْنَ الرُّكْنِ وَالْمَقَامِ
"The people of Mecca will come to him and take him out while he is in a state of duress and pledge allegiance to him between the Rukn and the Maqam"
The words Huwa Kaarihun do not necessarily mean "he will run from that responsibility", it only means he is being forced to accept the bay'a without first asking his consent.
Logically, a person can be compelled to do something without first being asked to consent, and that does not necessarily mean that he is against it.
Nor is it an argument that the Mahdi is appointed by the public and not Allah. Actually it means that the people will recognize the Mahdi and see that he bears the foretold signs within him, so give him the bay'a without asking him to consent to it, because it is a matter divinely ordained by Allah.