I'm astonished Babylon 5 hasn't been mentioned here, since it must have been a risk at the outset. The writers knew where they wanted to take the show and were given the leeway to go and do it. In a way it was only spoilt by the fact that having got to the end of the story in a satisfactory manner, the TV company then commissioned another season, which must be just about the only time this has happened in sci fi television history.
I have the opposite view. TNG had almost nothing new and while TOS pushed boundries TNG played it safe. While struggling through two bad seasons even the cast evolved to a model of the TOS cast. Data is Spock. Jordie is Scotty. The doctor is the longtime friend of the captain. etc... Even the stories were safe. The closest thing to gay rights was a story about Beverly falling in love with a Trill, then rejecting the Trill after it was moved to a female host. Umm, did I say gay rights? Never mind. That story was almost the opposite. Anyway, TNG was vanilla flavored Star Trek. Loved by the masses but not very adventurous.
I know that some fans looked at TNG hoping for an explicitly controversial "Blood and Fire" type story, but I think the way in which the show pushed boundaries was more gentle and subtle. For instance, Data, while quite possibly modeled off of Spock, sought to become more human while Spock tried to resist his human side. Both the ideas of a friendly android and of a computer who sees humanity as superior to technology were almost unheard-of in SF (at least in SF TV) in 1987. Most androids up to that point were either completely obedient, humorous or menacing, and none sought to put humanity on a pedestal the way Data does. For social issues like gay rights, TNG had "The Outsiders," which explored the issue through heavy metaphor. Sure, DS9 would later deal with the issue a bit more explicitly, but the fact that SF TV dared to touch the issue at all was ground-breaking. In addition, "Violations" touched on rape, "The Loss" on disability and "Ethics" on ritual/assisted suicide, all topics that were taboo to most of TV (especially SF TV) up until that point. Okay, so maybe I was able to come up with more concrete examples...
I don't agree with the statements in the OP that TNG was unique to television or that it took risks; it wasn't and didn't. TNG rarely explored any SciFi ideas, rather it lifted all of its ideas from other genres of TV that are completely irrelevant to SciFi concepts, like soap opera-type drama (only minus the continuing storylines of soap operas). There's nary an original idea anywhere in TNG. TNG was successful only because when it aired, for some bizarre reason. people had a higher tolerance for watching unoriginal, rehashed ideas. I do agree with the OP that the tolerance for unoriginal, rehashed ideas has decreased over time, which is a factor in why VOY and ENT, SGU etc. flopped. However, it does not follow from them flopping that TNG didn't flop because it was better or different. The holodeck is a prime example of TNG's complete unoriginality. It served no purpose whatsoever other than to let them make filler episodes that have absolutely nothing to do with SciFi, and which are exactly the same as episodes of any other non-SciFi TV show.
Ignoring the above post in favor of a sane opinion, TNG did take a major risk in its very premise of abandoning Kirk and co for a new era of the Trekverse and in basically CREATING a Trekverse beyond what we saw in TOS. These sorts of spinoffs that put the original so far away tend not to work, but TNG clearly avoided that and managed to create a bigger Trekverse than what TOS had. Yes, it showed off ideas that were before unknown to televised sci-fi. Haters can whine all they want about how it doesn't measure up to sci-fi literature, but that's simply down to the core differences in mediums and not a failure of TNG. There's plenty of originality in the show, and even in its spinoffs. Soap opera melodrama, EVERY show in existence has this one way or another so it's simply hypocrisy and/or stupidity (mainly both) to make it seem like TNG was alone in that regard. TOS "lifted" just as much and was just as guilty of "non-scifi" for most of its run. I happen to like SGU, despite the irritating characters and such. More than I ever liked NuBSG, funny that hm? The holodeck, good idea that got overused a little bit. But not a ruined idea at all. It's no different from powerful aliens making weird illusions and other stuff.