Bill O'Reilly and Cal Thomas have both opined on what a really fun idea that is, just like in the movies.
Middle East Mercenaries
Professional warriors have been called the Second Oldest Profession. The most famous mercs in the Middle East were the Khwarezmiyya who were hired by Genghis Khan after he had destroyed the Persian Empire. They were also hired by the Kurdish Ayyubid Empire to drive the Crusaders out of Jerusalem in 1244. Wait. That's not at all what Cal and Bill want.
What Bill and Cal want are white, Christian mercenaries. Men like 'Mad Mike' Hoare. Hoare hired himself out to quell bush rebellions in the Congo during the 1960's. Later in life he and a troop of South African soldiers of fortune were hired (through a variety of shell organizations) by the CIA in 1981 to overthrow the government of the Seychelles. Their war never got any farther than the airport tarmac and they had to hijack a plane to escape.
Of course, modern mercs are big business. G4S Solutions has the seventh largest army in the world with over 650,000 employees. Blackwater (they change their name every few years) along with her many sister forces within Constellis Holdings boast a fighting force in excess of 30,000 mercs who are not afraid to murder, rape, and maim.
I suspect O'Reilly and Thomas are examples of pundit payola. They were probably paid to promote the business of corporate mercenaries.