The verse about Prophet Ibrahim (a) being an Imam is significant in Shia thought because:
1- It indicates Imamate is a divine position. God chooses Imams, not the people. God chooses such religious leaders, not the people. The caliphate or Imamate after the Prophet (s) must be by divine appointment, and not a matter deferred to the people. In 2:30 and 38:26 the Qur’an makes it clear that the position of Khalifah is also by divine appointment. This demonstrates that the 3 caliphs after the Prophet (s) were not rightful caliphs. They were not appointed by God through His messenger. Imam Ali, to the contrary, based on numerous authentic sources, was declared by the Prophet (s) to be his Caliph, Wazir, Imam and the Mawla after him.
2- It indicates that one who is a ظالم, meaning one who is unjust by committing acts of injustice, is not qualified for this position. We believe Imam Ali was infallible and the only caliph qualified for this position. The others were not infallible.
Secondly, in our Sahih hadiths, the Prophet (s) explicitly mentioned who the 12 Imams are. He made references to them, but of course the Umayads and other enemies of the Imams tried to bury such narrations. Just because Bukhari and other Sunni works don’t mention these clear hadiths doesn’t mean the Prophet did not say them. Just as Jesus names his successors, so did the Prophet. This is well established in our hadiths.
Third, the Prophet made it very clear in the famous Hadith of Thiqlayn that his Ahlulbayt or progeny are tied to the Qur’an and will never separate until they meet him at the pool on the Day of Judgment. This hadith confirms they are infallible, for if they were not, then they could not be tied to the Qur’an as such. If they would sin, they’d separate from the Qur’an.
As for verse 33:33, though it directly includes the Prophet, Imam Ali, Lady Fatima and Imams Hassan and Hussain, the Prophet and Imam Ali and Imams Hassan and Hussain clearly stated that it also includes the other 9 Imams. This is well established in our hadith sources.
Furthermore, we know that 33:33 doesn’t include the wives of the Prophet (s) because in Sura Tahrim (which was revealed after 33:33) the Qur’an condemns two of the wives of the Prophet for their conspiracies against the Prophet, and it is rationally impossible for them to be a part of 33:33 and thoroughly purified by God yet they would do such disturbing things that warranted condemnation from God. How could their hearts stray (66:4) when they are thoroughly purified by God? And there is no doubt Aisha fought Imam Ali at Jamal. How could they both be thoroughly purified when they both fought each other? This creates a discrepancy in 33:33, and there are no discrepancies in the Qur’an.
In sum, our Hadiths indicate the Prophet clearly mentioned the 12 Imams. If you ask why they weren’t clearly mentioned in the Qur’an, then my response would be similar to these responses here: