What are the implications, effects, and ramifications of considering the opening "Allahu Akbar" (Takbirat al-Ihram) a pillar (rukn) according to the majority of scholars, and a condition (shart) according to the Hanafis?

The majority of scholars hold that the opening takbir (takbirat al-ihram) is a pillar and an integral part of the prayer. However, the Hanafis and the Shafi'is, in one of their views, consider it a condition external to the prayer. Nevertheless, it is unanimously agreed that it is a pillar in the funeral prayer (salat al-janazah). This difference leads to subsidiary disagreements, such as the permissibility, according to the Hanafis but not the majority, for a worshipper to begin prayer facing other than the Qibla or while carrying impurities, and then rectify the situation. Similarly, the Hanafis, unlike the majority, permit beginning the takbir a few seconds before the prayer time actually commences.