Nah, it's pretty safe to say this is simply the way the author wanted to take the story. It's more than obvious the author's extend of military knowledge is limited to what he has got from books and videos and other series. In reality armed forces send enough men and resources to get the job done. Only a nation fighting a losing war go for suicide missions and undermanned missions hoping for a miracle.
No, they would volunteer for their own sake. Unless there was some gay person doing it for Itami, but so far we haven't seen any. He has no close female soldier underlings, except for the psycho, who would die laughing if it happened in battle. It'd be highly arrogant of Itami to imagine they would do it for him. The local girls are doing it for Itami, like KrayZ said, although like the psycho woman, Rory wouldn't turn down any chance to fight (except fighting Hardy, probably).
As I understood it, he earlier refused the idea of a resource scouting party. You can't really expect anybody to take seriously that this one man is qualified for it unless he has a master's degree in geology as well in addition to everything else. Not that it would make this show any less hilarious.
He was supposed to be on his way to the capital, after being commanded to return there. Yet he decided himself he's not going there. Instead the HQ commander will soon learn Itami took a car, weapons, and food and went who knows where (since only the dark elf knows where). That is not how the military works.