Let's suppose I agree with your interpretation here. As it is according to you belief that Allah Ta'ala grants Imamah to deserving people without any external interference. And the infallible Imams by their status of infallibility know that they'll become Imam eventually, in specific when the previous Imam passes away. In addition, you believe that the Prophet (sal-allahu 'alayhi wa salam) has foretold about the 12 Imams. So why does an Imam has to make du'a to Allah Ta'ala for becoming an Imam when we know the du'a has nothing to do with Allah Ta'ala pointing him an Imam? According to your understanding, the Imam is asking for perfection and infallibility as a normal person can't do this according to your own beliefs. However, such du'a is already redundant for an already infallible and perfect person! This is all inconsistent or incompatible with your doctrine!
Dua is means to seek nearness to Allah Ta’ala and Sunnat of the representatives of Allah (swt). All finite beings, including the representatives of Allah (swt), have the inherent shortcoming of not owning anything of their own but depend on gifts bestowed to them from Allah. And thus there is a pattern of Duas in the Quran where the greatest of the Prophets of Allah (swt) are beseeching the Almighty for the blessings already promised to them. For example, according to both Shia and Sunni aqeeda, Prophets are infallible and free from sins, yet we see them asking for forgiveness in the Quran:
Hazrat Noah
[71:28] "O my Lord! Forgive me, my parents, all who enter my house in Faith, and (all) believing men and believing women: and to the wrong-doers grant Thou no increase but in perdition!"
Hazrat Ibrahim
[Yusufali 60:4] ….. when Abraham said to his father: "I will pray for forgiveness for thee, though I have no power (to get) aught on thy behalf from Allah." (They prayed): "Our Lord! in Thee do we trust, and to Thee do we turn in repentance: to Thee is (our) Final Goal.
[Yusufali 60:5] "Our Lord! Make us not a (test and) trial for the Unbelievers, but forgive us, our Lord! for Thou art the Exalted in Might, the Wise."
[Yusufali 14:39] "Praise be to Allah, Who hath granted unto me in old age Isma'il and Isaac: for truly my Lord is He, the Hearer of Prayer!
[Yusufali 14:40] O my Lord! make me one who establishes regular Prayer, and also (raise such) among my offspring O our Lord! and accept Thou my Prayer.
[Yusufali 14:41] "O our Lord! cover (us) with Thy Forgiveness - me, my parents, and (all) Believers, on the Day that the Reckoning will be established!
If you keep the above context in mind then you will be able to understand the the verses 25:72-75, Insha Allah.
And where did you read that its a Shia belief that a normal person cant ask or aim for complete protection from Sins?