Police are unionized state personnel and will uphold and protect the power of the state over the citizenry. Enforcement and Intelligence gathering. They are not elected as the county Sheriff's departments are elected.
US military? Volunteer in service to the country. TEA Party? Volunteer in service to the community.
But getting back to allowing the police onto the planes without screening, would you not agree the jihadists would be looking for terrorist opportunities? And that "trusted" (or "sworn" as you state) public employees would make a high-impact terrorist statement? That's my point. And for that, these people should be subjected to MORE scrutiny rather than less.
Another option is profiling as you suggest (and I support) and the third option is blaming all this TSA nonsense where it belongs: on the Moslems. Ever since Yasser Arafat's group starting hijacking planes in the 1970's, it's been MOSLEMS who have a particular affinity with the flying craft.