There had been multiple cases of individuals that needed the remival of a huge piece or a complete cerebral hemisphere that remain functional. Although they are never completely neurologically healthy. We need both brains for our correct complete biological, social, and practical function.
Memories have nothing to do with the proper function of a brain.
The brains needs the memory cache as well as the processing system, in a similar fashion for computers. What use is a 1 Tb hard drive filled with information without the motherboard? And what use is the best motherboard available without at least a modest hard drive for information storage?
There are diseases that selectively damage areas of the brain that are related to information processing and judgment. Limbic lesions impair the capability to process new experiences into knew memories. Wernicke area lesions impair the capability of understanding words even if the patients already knew how to read and write.
The brain works as a whole. Every system and every area is important.