I don't think Jack White is that awful. I think he gets flack because he's popular and it really is cool to hate on the popular things. In my opinion, there are a lot of bands that are a lot worse for rock. The Monkees, Nickelback, Evanescence, Five Finger Death Punch, Good Charlotte, I can go on and on. Now, I'm not going to go out on a limb and say Jack White is absolutely amazing, but there's no denying he has enough talent to deserve the recognition he gets. I think he even deserves a bit of extra credit, because unlike a lot of musicians, he's willing to take on new projects every few years. If he really didn't care about what he does, I don't think he'd be willing to do that.
[tongue only slightly in cheek] The Monkeys... despite being a manufactured band had a longterm influence. Like it or not - in a weird sort of meta way... a lot of people can hum or sing the monkeys theme song.None of them had/will have any particular longterm influence.
Some of them had a pernicious short-term influence, though. Late 90s-early 2000s alternative rock was so stupidly over the top we got a decade of twee and anemic rehashes of earlier eras we haven't quite recovered from as a reaction. Unlike the reaction to stadium rock, which was great, we got rock music that was afraid to... rock.
And that is why they're bad bands. Anything that is remotely good will inspire people to be creative, to emulate yet experiment. They'll be remembered 20 years down the road. Jack White? He'll probably be remembered and people will still enjoy his music. The bands I've listed? They'll only be remembered for being awful. That's part of the problem though. They're awful bands that are easily marketable. They're out there to make the music industry a quick buck and they prove that band, easy formulas are the way to do it. In my opinion, that's 100 times more damaging to the world of music than anything Jack White has done.None of them had/will have any particular longterm influence.