Her young age is central to my point. The Prophet (SAWS) died at age 63, so she had 44 years of her life after the Prophet (SAWS) died, in a time of great fitin (tribulation). The religion only began to be formally codified, and written down during the 3rd Caliphs reign, and the presence of Aisha (RA) is absolutely crucial to this part of the religion. The Arabs back then would memorise great deals of information, and transfer of knowledge was done orally. Aisha (RA), in terms of memorisation, was one of the best, coupled with the inquisitive nature (as all youths have), her scholarly outlook was held in extremely high regard. The nature of Aisha (RA) is well documented. And as I said, without her so much would have been lost. The fact that she was around for 44 years, outlived her husband, the 1st Caliph, the 2nd Caliph, the 3rd Caliph, and the 4th Caliph was a huge reason why Islam managed to persist.
Aisha (RA) and Abu Hurayra (RA) had conveyed upwards of 4500+ Hadith, and Aisha (RA) specifically lived with the Prophet (SAWS) in the last 10 years of his life as a prophet. She is a central figure, and it had to be someone young to keep the religion intact during transitioning periods.