I think the problem is that "Strong" in the context of character has almost no meaning. What is a "strong" character? Is it one who is physically strong? Is it one who is emotionally strong? Is it someone who takes action when it is necessary?
The problem is that "strong" means multiple things, and none of them are synonymous with "good."
You can have a physically strong woman. Say, Korra. But is Korra a good character? I would argue that no, she isn't. Too much of the plot contrives itself to vindicate her, she herself is not a well developed and interesting character.
You can have an emotionally strong woman. Let's be topical here and say Lin Beifong. She's stoic, in control of her emotions, makes good decisions. Is she a good character? I'd say yes, but that's more because the plot doesn't betray her narrative constantly, it isn't really because she's a strong woman, it's because her arc made sense.
And you can have a woman with initiative who acts to protect the people she loves/defeat her enemies/achieve whatever. This is virtually any female protagonist. How many good female protagonists can you think of? There are a few, but it isn't all of them, so this is obviously not synonymous with quality either.
Becoming bogged down in what "strength" is and how strong female characters should be ultimately misses the point of character writing. Interesting characters, good characters, characters who are remembered for their quality and who influence peoples' work, are not made so by how "strong" they are, they are elevated by the quality of their writing, the attention to narrative detail, and the consistency of their characterization.
It is a sorry state of affairs when the only question anyone is interested in asking about a woman is whether she is "strong" or not. I did not read the Brothers Karamazov because I wanted to read about strong independent Russians who don't need no Tzar, nobody watched Les Mis because they wanted to watch a thief flaunt authority. Good characters are about good characterization, not about buzzwords and labels.
Really if you want to point to any one thing that has hurt the depiction of women in media, it is this obsession with "strength." It's almost Freudian, as though people subconsciously believe women to be inferior and so scrape to compensate for this in fiction at the cost of quality and narrative integrity. It reminds me of the 1980s when they stuck obnoxious token black characters into everything, unwittingly creating horrible stereotypes that persist to this day. It would have been better to do nothing. It is better to be underrepresented than misrepresented.