At best, “support our troops” was a version of that dumbass magical thinking that, in earlier times, held that the U.S. lost in Vietnam because Americans didn’t clap for Tinkerbell, err, I mean, support the war. Mostly, it was a thought-terminating cliché.
Yeah, as you rightly point out, it was never about the soldiers themselves.
Sometimes you do it the hard way to send a message.