Some of it is preference.
Some of it is necessity.
With veg tanned leather you could do any of the three techniques you mention.
If the leather is really thin people usually fold it.
If it is chrome tanned it is hard to get a good burnish so people will use edge dressing or edge paint.
Hope this helps, I haven't used all these methods myself. The two wallets I've made were both from chrome tanned with burnished edges. One came out good, the other (first) one, not so good.