There are a couple of major problems facing The New Day
One of the major problems happen to be fans themselves. Let's be honest, a shitload of fans already had their minds made up not to like The New Day from the very moment they saw the group's first vignette. It's become fairly common these days for fans to condemn a wrestler or faction long before said wrestler or faction debuts by their vignettes; a lot of fans simply crap all over something and don't give some stuff a chance from the very start. A lot of these same fans are also pretty limited in what they want to see in terms of a gimmick: just about every guy is supposed to be some kind badass with some sort of edgy "I don't give damn what anybody thinks" swagger and persona. Anything other than that? Many of those same fans piss all over it.
Another problem facing the faction is the nature of the faction itself really. They're "positive" people trying to deliver a "positive" message in an energetic sort of way. They're happy, smiling babyfaces and a faction of happy, smiling babyfaces usually doesn't rise beyond a certain level. The top factions have pretty much always been heels: The Fabulous Freebirds, The Four Horsemen, The Heenan Family, The Hart Foundation, the nWo, D-Generation X, The Nation of Domination, The Ministry of Darkness, The Corporation, Evolution, The Shield, etc. have all primarily been heels. Even if they reformed later on as babyfaces or turned babyface, they'd established themselves as stars and forces.
Rebranding The New Day as a new version of The Nation of Domination won't work in this day and age because, frankly, society is too politically correct to tolerate it. A faction of militant, pissed off black guys patterning themselves on The Black Panthers would probably work just fine in smaller promotions because, frankly, smaller promotions don't have WWE's audience. A problem with WWE being the biggest wrestling company in the world is that whenever something bad happens in wrestling, WWE is who winds up catching all the shit when it hits the fan here in the United States. Not TNA, not ROH, not the modern NWA, the WWE. When you consider the various media stories over the past few years in which race has been a huge factor like the Trayvon Martin case, those four black teens who were shot at in their SUV at a gas station in Florida by a middle aged white guy, the clusterfuck of Ferguson, MO, the WWE creating a militant, African American faction would be construed by some fans watching as an attempt to profit off these issues. And you know that media outlets would pick up the story, opportunistic journalists like Nancy Grace would be covering it, it'd be all over social media, etc.
Basically, WWE would be raked over the coals for capitalizing on "racial tensions." Remember the crap WWE caught a few years back in regards to Jack Swagger & Zeb Coulter's characters? People were going ape-shit all of a sudden and accusing WWE of being racist or exploiting racial issues. You also have to remember that, as unfair as it is, there's some strange media double standard when it comes to WWE because other TV programs are able to get away with capitalizing on "racial tensions" and using it as part of their storylines. But, for whatever reason, people seem to forget or ignore that pro wrestling storylines are scripted.
TNA, ROH and pretty much any independent wrestling company in the United States could create a faction like the NOD and it'd be okay, primarily because mainstream media wouldn't know about it or, even if they did, those companies are much to small and too low profile for them to bother. Targeting WWE would give them ratings and generate interest because of WWE's standing. People can debate about who is the better company, who the best wrestler is and all that, but the simple truth of the matter is that when most people in America think of pro wrestling, the first name that pops into their minds is WWE. Sometimes, it's the only name that pops into their minds. That's a good thing for WWE but, at the same time, it's a bad thing as well as the company's success is something of a double edge sword.