I started wondering about this for no particular reason I can think of. Who’s idea was it? Was it supposed to be symbolic of something? Did they just start passing out pamphlets at rallies titled: “Forget everything you THINK you know about public greetings!”?
By the time of Constantine Christianity was big already. They just stopped fighting it and embraced it, better to be the one controlling it that the one steamrolled by it.
Perhaps, like the Romans, some people just enjoy lying about weird foreign cults that worship the wrong things.