What is the wisdom behind the existence of weak and authentic hadiths, and why were not all hadiths preserved like the Qur’an?

The Holy Qur’an was preserved by definitive widespread transmission (tawatur qat'i), but this was not the case for the wordings of the Prophet's Sunnah. This is because transmitting the entire Sunnah through widespread verbal or conceptual transmission would cause immense hardship. Therefore, the Ummah sufficed with transmitting individual narrations (ahad) that met the conditions of authenticity, and established rules and principles to distinguish the authentic from the weak, which is what distinguished the science of Hadith. This distinction is a manifestation of the preservation of the Prophet's Sunnah. Nevertheless, the verbal and practical Sunnah that is essential for Muslims has been transmitted authentically, and a large portion of it has been transmitted through widespread transmission (tawatur).