I think the reason for them not having any brands on certain wrestlers is because they don't need it as much as other companies do. Most of the wrestlers are very happy with what they're getting paid and get to do certain brand deals on social media and TV on top of that anyways.
Besides, it would have to be a really neutral brand that could work on either a babyface or a heel, given the nature of the business where characters and their beliefs can change at any given time.
The reason why it would have, somewhat, worked for Punk was because his character at that point was being a guy who wanted to make more out of his name than what the company wanted. So for him to have a sponsor would have added to that rebel persona. But then again, Punk also wanted to come back in MMA shorts, which would have been god awful for a guy who'd still wrestle the traditional style, so I get why WWE tried to kinda back out of that whole mess.
Personally I wouldn't have a problem with it, as long as you choose the right people for it and who's attire would fit a brand well, like Styles' or New Day's for example. But due to the fact that pro wrestling is a really special thing, there are a lot of people that are already out of question just because of their gimmick alone, so I wouldn't expect people like Taker, Bray Wyatt or Braun Strowman to come out with a 5 hour energy logo on their attire
