Why do coaches do pick/ban instead of analysts?

Title. If it's the analyst's job to create battle plans and formulate the pick/bans for teams, while the coach is implementing these things in practice and helping the team communicate/synergize...why doesn't the analyst do pick/ban? Wouldn't it be more effective for the person who is behind the strategy, and also be better at altering the strategy on the fly if needed, to be on stage? Or, do I have a fundamental misunderstanding of the roles of these two positions?
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