Because it is not traditional to plait them. The Bedouin never plaited them and the long, loose, flowing mane and tail is part of the 'look' of the breed.
It's not just Arabs - most pure breeds are shown in their natural state - it's really only "types" (hunters, hacks, riding horses, riding ponies etc.) that are shown plaited i.e those that are supposed to fulfill a certain purpose. Bound to be some exceptions but I think that seems to be the general rule.
I have no idea, tradition? Perhaps because their long manes and tails flatter them more than pulled and braided, and anyway, how stupid would that high tail carriage look braided! Some arabs look very smart plaited and pulled, anglos have to be for showing
Perhaps because they are a pure breed? You could ask why M&M breeds are left natural (OK with tweaking here and there) as well.
Whatever, I am very pleased that they are, I can't be doing with pulling and trimming, a 2 minute arab plait for exercise does the job.
As with M+Ms the mane and tail are a feature of the breed and hence are left natural. Anglo and part bred Arabs would be trimmed and plaited, as are part bred M+Ms.