If you restrict access for administrators to using sudo, then all root commands are logged, provided you disallow something like "sudo /bin/bash" and plug up holes such as entering "!/bin/bash" in vim.
The bash history is not intended to be a full log. It may fold repeated commands into one, and it is limited to a certain number of lines. It is a convenience, used to recall previous commands, such as using [ctrl]-R or !-5.
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