Very well, then, I will pose the same question Syed Zafarullah Shah (from Takbeer TV) posed to Hassan Allahyari which caused the latter to run in all directions and mumble something incoherent from a text (Al-Kafi) which is not hujjah upon us.
You said that the Qur'an "doesn't state all righteous people will be Imams" and you also believe that only Allah (swt) appoints Imams. Then why the following supplication in Surah Al-Furqan verse 74:
"And those who pray, 'Our Lord! Grant unto us wives and offspring who will be the comfort of our eyes, and give us (the grace) to lead the righteous (Imama).'"
If Allah (swt) appoints Imams, then why are we making this supplication almost on a weekly (if not daily) basis?
If we look at the context, it's referring to people's ignorance of Mohammad's station, and their over all blindness to the station of God's chosen ones. So when it says "And the servants of the Rahman....", it's not refering to all servants of the Rahman.
We can prove that three ways:
1. Context it was related to specifically the servants of the Rahman they were saying would be given mansions, etc, if they were actually chosen to guide humanity.
2. Mutaqeen are good servants of God, but not all of them would be included, because the prayer is to be an "Imam" of Mutaqeen (so if all mutaqeen were Imams who is left to be lead?)
3. Other verses showing that it's not for us to say who is to lead us and guide us and who is the path way to God, for example, Abraham was a way/course (ummatan) to God, because he has clear proofs and evidence. If we can decide who is our guides and leaders and examples to follow and imitate and be lead by, then there would be no need of Prophets and revelations from God.
If you are Shia, there are hadiths that verify it refers to God's chosen ones.
The very next verse says, "Those are the ones who will be rewarded with the highest place in heaven, because of their patient constancy: therein shall they be met with salutations and peace". Here Allah (swt) is saying that the righteous will be rewarded whereas you are saying that not every righteous person will be Imam when the Qur'an teaches us to supplicate for our children to be Imams (and guarantees reward for the righteous).
If all Mutaqeen/righteous are leaders, who is left to lead the righteous/mutaqeen?
It is the core of Sunni Islam to understand everything holistically just like your own established beliefs (regarding Imama) fail in the light of the Qur'an.
The core of Sunnism is to disconnect Quran verses from one another, and disconnect hadiths of the Prophet from the Quran.
Isolate and interpret by desires. That is all there is to it. It's nothing but huffing and puffing and making blindness as if it's a virtue.