Firstly, your use of the phrase 'in the west' implies that outside of the 'west' there is some different, better elementary education system. This has not been my experience in India, where capacity for rote memorization is regarded as equivalent to intelligence from an early age. What countries fit your boundaries of 'the west'?
Secondly, school serves as a valuable social and educational center to most children. Even though elementary education is imperfect, it does not mean that a viable solution is to simply do away with it. In fact, I think the social interaction with other children of similar age is extremely important to developing social skills and friendships.