Do we actually believe that "big pharma" (in the form of 3 companies that make US approved vaccines) have greater influence than all of the collective industries
They only need more influence in key places like FDA and CDC, not more influence overall, to push health policies.
The FDA and CDC are not involved in vaccine mandates. Even the coming federal mandate is through OSHA. They issue recommendations, but so do a lot of other influential people and organizations.
That said, this is a real phenomenon and worth bearing in mind when doing this type of reasoning.
They only need more influence in key places like FDA and CDC, not more influence overall, to push health policies.