Well, dependent on someone else, or being independent or being strong or weak isn't the issue. There's probably many sexist depictions of strong and independent females if it's just used as a fetish item or especially the "she needs a man anyways" tripe. I think Clannad barely averted that with Tomoyo (though Tomoyo After not as much and can be safely ignored as just being a pointless what-if spinoff.)
What matters is choice. This means that anything from burqas to skimpy swimsuits, from prudery to blatant sexuality can be sexist if it's regarded not as a choice on the persons' part but to solely please other people. But as you've noted this gets twisted around so much to fan desires. It would be kinda ironic if Madoka would spiral down even faster than Nanoha did, but then again I have like negative respect for Shaft/Shinbo at certain points so it's to be expected. In either case, yuri fetishism has at the same time brought to the forefront but because it's being fetishized can never be taken seriously outside people's dark bedrooms. It's been emphasized for all the wrong reasons.
Anime often has so much trouble just appreciating platonic relationships too. I could list all the shallow and forced attempts at romance just to create drama and pairings but that would be too tedious. It's no wonder I scoff at romantic elements so often.
Of course, male characters have the same problem. As you might have pointed out, there's so much expectations for them to all be conniving and cold blooded, and violent. Where a guy that doesn't solve his problems through violence and destruction is criticized as being not a man. Besides, you don't need a body count or life threatening injuries meted out to others. Hell, look at Akagi. He hasn't killed anyone; and anyone that did get fucked up dealing with him brought it upon themselves. And I bet nobody brings this up, but he does often pick the solution that doesn't result in more bloodshed. (Such as vs the punks or Urabe... he could have easily killed them all if he was a true asshole. But he didn't.) Though at the same time I guess Madhouse did make him seem more cold in the anime-- they cut out some of his more human moments. There's still a few in the anime, and I find those actually pretty good to round out his character-- in the end he's just a human.
Ultimately, to make good characters you need to make them appear to have their own will and sentience. Otherwise, you get a lot of junk and characters that aren't people-- they're caricatures. And I have never been forgiving of such things.
I probably will check out the movies. After I get through the TV material.
Certainly too many people twist what Nanoha and Fate stand for to suit their twisted perversions (and inevitably, those making the material became a party to this in recent times), which in term causes the resident reviewers of Mount Pious to slam the franchise. But meh, their loss. I think overall the better times of the title stand up well to the test of time. And as you said, Nanoha and Fate were able to rely on themselves and each other in turn - they didn't need a guy to be a crucial part of their success/the muscle of the operation.
And as I said to Triple_R, there are far worse things that can happen to a female character.
Well, it's certainly a very novel series. I think they did create things that were unique and stood out. In particular, Nanoha the really charismatic lead that isn't afraid to take charge is a far cry from the incompetent and scared audience surrogate that seems to populate this kind of show. Fate is put out as a tragic character but her internal and external conflict don't define her as a person as that would just be rather contrived and manipulative. Instead, it's used as a stepping stone to bigger and better things. If they took anything of value from mecha anime it would be the heated conflict between those with different ideologies that are fighting for their own cause and that has that whole "in any other universe we'd be friends" or some crap, but very prevalent in A's.
Recently realised why it is I am neither here nor there about Free.
As far as I'm concerned, it isn't FABulous at all. I wouldn't even call it pretty. Sure there's plenty of bare-chested bishie hunks getting wet, but it's all very meh.
Looked through my list of anime and I found one title that I did classify as good FABulous for my own tastes - Hanasakeru Seishounen. The odd title has a FAB character but that title was the ultimate reverse harem gem.