That goes back to something I suggested a few weeks ago - split Batman into two characters. Have Bruce Wayne be the "bat-god" who is a member of the JLA and in the Batman monthly series he deals with villains like the league of assassins (Ra's, Talia, Bane, Damian etc.... the Dark Knight league), Hugo Strange, Vandel Savage etc... (ie - global threats), maybe even armor similar to Arkham Knight. While Dick becomes Gotham's Batman, who deals with the mods and villains like Two-Face, Pengiun and Joker.
I think giving "street level" characters powers can be tricky (not impossible but tricky), if they become too powerful you lose that street level feel to them. If they can handle regular people too easily.......thats not good. You also wants to keep an element of danger around those characters. Once a character is impossible to hurt or kill.......
This seemed to be the approach in the past. There was a kind of Chinese wall between the Batman in the team books (JLA, B&B, WORLD'S FINEST, THE OUTSIDERS) and Batman in his own books (BATMAN, DETECTIVE, various one-shots and mini-series). When you read Batman in a Justice League adventure, you just accepted that Batman was different in those adventures; whereas, in his own books, he handled street level crimes and you didn't expect some super-hero to swing by and solve the case for him.
It's really not that difficult.
And it can be done successfully. Look at the evil empire (Marvel). There there's a shed load of variety in the guys that see street level action. Spider-man sees a load of street action...and at 40 times human speed and strength, enhanced agility, webs, warning sense (NB about as reliable as my first car) is a veritable power-house. Daredevil has one of most interesting power-sets in comics. Powerman has his near invulnerable skin and respectable strength. Even dear old Iron Fist can do useful stuff with the chi. And there's Hawkeye for those that insist on the non powered plucky under-dog. Then there's the Punisher as the example of the non powered guy who will use any advantage he can get his hands on to come out on top.
I quite like Batman as the non powered detective. But just wish there was some more variety in powers and attitudes in the street level set. Clearly DC can do it when they put their mind to it. The 2004 Manhunter series (before it lost the plot) was more or less a model of what a modern street level hero should be like...Kate was a low grade meta (increased strength, agility and physical recovery powers), who made very sensible use of high tech back-up. Jeez I liked that series.
The original Question had urban shamanic powers in a mini series. I forget the explanation for it but it was very cool and made sense. Made for a good mini series too. I don't think Montoya had any powers though. So it's kind of a step back. I like Montoya but I miss Vic
My knee-jerk reaction is to say no to powers but when I think about it, yes I'd like to see someone like Huntress get a simple low-level power set. Even something very simple like enhanced vision (fits with the name). It might feel weird at first but I'd get used to it if the stories are good.
I also like Moon Knight's power set.
I said it can be tricky, not difficult. ANd of course i can be done, has been done, and will be done again. But you also can't just make a hero with X powers and say "street level" you do have to be aware and make sure the character you'd creating will fit in the way you want him too. Some people are saying plastic man should be one of these lower powered heroes, even though he is one of hte most powerful heroes in the DCU.
I really perfer Batman to Bat-god as well. If DC was willing to remove him from Justice League books and have him one of their top characters just in his own corner of the DCU (think how Wolverine and Spider-man used to be), I'd be VERY happy with that.