Me and my kids have worn air jackets for quite a while now. We all have Ht-Air brand which are very lightweight, they don't feel at all restrictive.
For cross country you are supposed to wear a protector as well.
One of my kids had a straightforward fall off a green horse who hadn't ejected anyone before and although she wasn't injured the horse kicked her in the back as he found himself riderless, panicked and turned and there was a hoof print on her jacket - she didn't have a bruise.
I once broke part of my spine and damaged my spleen falling from a horse and an air jacket could have prevented that.
They obviously don't prevent all injuries and there are disadvantages to them but they do seem to prevent the worst types of injuries providing protecting for most of the torso and the internal organs.
The trainers at our yard recommend them, especially for jumping. Remember that 40 odd years ago people sneered at having to wear a hard hat.
As for the bang - it can startle the spookiest of horses but it's no louder than if they knock a jump down or even clip it.
A tip if you do get one: don't forget to un-clip it before dismounting. The canisters are expensive. The only time I've seen a horse spook from the noise was a forgotten airbag at dismount. He was standing there, end of class, all chilled and then suddenly bang.