I don't understand why you wouldn't be able to live without one. In AQHA and APHA shows, yes the thing right now is fake tails for riding classes. In some of the AQHA and also schooling shows following AQHA rules, halter horses will have a fake tail in. I agree with Jessabel that it takes away from the horses hind end when you have this poofy thing hanging off their butt. I have shown without a fake tail and placed top 5 so I think it's just more a personal preference.
Around here, Showmanship/Halter are usually at the beginning of the day, so it would be pretty easy to show in those classes and then put in the tail for your riding classes. Just PLEASE make sure it's in right. We see a lot of youth riders around here with them in horribly. It looks so bad lol
As far as the mane, Jessabel was right again. It's to show off their neck.