Why do we pray in this specific manner of takbir, prostration, and standing? And isn't reading the Quran and making supplications sufficient instead?

Absolute submission to Allah and His Messenger is obligatory concerning the rulings of the religion, for religion is built upon the necessity of hearing and obeying, and not objecting to the commands of Allah the Almighty, just as is the case with trusting a doctor's words. Faith is not established except through absolute submission to Allah and His Messenger, and any questioning of the reasons behind legal rulings may lead to their denial and to atheism. Prayer was prescribed in this manner to achieve complete servitude to Allah, to humble oneself before Him, and to delight in intimate supplication.