Is there anything that precludes us from giving the evaluation committee the technical and cost proposals at the same time?
I am not aware of any guidance that prevents giving the Source Selection Evaluation Team both the technical and cost proposals at the same time. In fact, the recently issued DoD Source Selection Procedures document discusses one of two methodologies for the technical rating evaluation process as combining the technical and risk ratings, with cost realism of course being an element of "risk."
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However, the rationale you already provided— preventing team member bias when assessing technical risk— is a sound one should you decide to separate the technical rating from the risk rating.