I don't think a lot of these criticisms are valid. You can't say that a lack of technical detail makes everything completely fake. In military sci fi, it is more important that they tell the story than that they explain how everything works. It's when things become inconsistent that it becomes a problem. It's one of the reasons I prefer the tech of the Abrams movies - they mostly ignore replicators. The ability to transform matter is pretty much the ultimate power. You have to ignore it if you hope to tell any kind of compelling story, and Trek mostly does except for when the replicator goes crazy. I think it was normally an RD Moore episode where the replicated food wasn't nearly as good as the real thing because he wanted to emphasize it.
A story can be based off of anything if the writing and execution is good enough.
The Lost Fleet is an entire series that is basically about that same concept. Nobody owes anything to old BSG because the basic story is as old as story telling probably even back to the great migrations of pre-history. All of the key details of old BSG were thrown away because the show sucked completely, and the new one is almost indistinguishable from it.
That lack of branching out from Trek itself is Voyager's biggest weakness. They weren't ballsy enough to really make it their own show, so they had a harder time making compelling new stories. Either that or the studio was too controlling...and I'm honestly more inclined to believe that. If there is one thing I hate it's how creativity is smashed by the studio. It's actually a good thing that Enterprise was so irredeemably bad that they were willing to bring in new blood and not be so limited. Also if they hadn't already been planning Voyager the way they did, we probably never would have seen DS9 which pretty much gave the finger to them every chance it got.
I do think that they could have gotten the sci fi part a bit better. Ultimate power in some ways and ridiculously primitive in others - compared to TOS anyway - wouldn't be so bad if there was some level of consistency throughout. It's one of the reasons that the TNG and onward tech manuals aren't what I go to - they were written by the designers, unlike the TOS manual which laid down the rules much more clearly.