He wasn’t put “in charge” of the documents, he only had access.
The main problem seems to be that Manning was one of many people who had access to this huge database of cables. The full database should only have been accessible to very few people. That is the same problem is many of the worst spying cases. For instance, in the Richard Hanssen case, just because Hanssen worked in counter-intelligence in the FBi, why should that grant him access to every one of our greatest secrets, which he had no need to know about?
The system for maintaining security over classified information should not be capable of being subverted by one weak link.