Yes, you could do this. The National Guard would fight you tooth and nail. The schools would fight you tooth and nail. The security firms would fight you tooth and nail. And most importantly, the Democrats would fight you tooth and nail. After 9/11, I sent forward a recommendation to place armed National Guard Officers on civilian passenger planes until they could train up more Air Marshalls. The silence was deafening. The business of the Federal government is to create jobs, and they did. You will spend a long time looking for the government supervisor who wants to keep his staff at the same level and be more efficient.
I like your idea, but would refine it thus:
Allow Armed Forces officers and senior NCOs (Regular, Reserve, National Guard) to carry (on volunteer basis) on flights after completing a specific training program. MOst flights have at least one on board, and we could save the cost of all those Air Marshals.