In this sentence (psycho-pass's line):
The 身柄 can be omitted and thereby result:
I really wonder the use of 身柄 and if it is really necessary.
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～の身柄を押さえる and ～の身柄を確保する are set phrases that mean "to take someone into custody". I don't know the story, but in general you cannot omit 身柄. If the chairperson is cooperative enough, this can be achieved even without touching him.
議長を押さえます would mean "I will (physically) press the chairperson" or "I will pin the chairperson (e.g. to the ground)", which is very different.