No.
More importantly, she doesn't really matter. What is her impact on culture? As far as I can tell, it's nonexistent, except that it helps the Kansas City Chiefs sell more tickets, and generate more TV advertising revenue.
Elvis effectively created the culture of the corporate pop superstar. Generations of young girls lost their minds, and would save up allowances just to go watch him gyrate his hips. Taylor's a mere inheritor of the estate he built.
It's not like Madonna who enraged half the country by juxtaposing religious iconography to sexually charged imagery from the world of couture fashion. The world was so obsessed with her that the Cosmopolitan became one of the ten most popular cocktails in this country for decades just because women everywhere saw her in a magazine holding a pink drink in a Martini glass. That's obsession.
Taylor hasn't put entire genres of music to bed like Doo Wop or Hair Rock the way The Beatles or Nirvana did. Michael Jackson was so huge everyone alive tried doing the moonwalk, and nearly everyone mistakenly thought he invented it, because that was how much power he had for creating new pop iconography. If a performer today whipped out a single glove, and slowly put it on, everyone knows the reference. What would you do for Taylor? Nothing memorable, there.
What movement is she leading? She's not exactly the sort of artist who would inspire a Woodstock, and a widespread rebellion of the youth against consumerism and war. That's what artists like Bob Dylan, Jimi Hendrix, Joan Baez, and others did. More broadly, entangled with those, there was the countercultural defiance of "The Man" and everything represented by that status quo by less politically minded bands, or more purely, those focused on living a life pursuing the bliss of sex, drugs, and rock n' roll. That was The Rolling Stones, The Doors, the Who, and others.
She's not N.W.A. or Public Enemy contributing to an entire race carving their voice into an emerging genre of music that was boldly content to define itself apart from White America, and what its majority considered acceptable.
I read an article just yesterday that observed Macklemore's recent song protesting the pushback against the pro-Palestinian protesters was special if for no other reason than it exists in an era of apolitical music. I can't say I'm eager to hear a bunch of whiny political sermons from first world brats, but that's a huge part of how the Civil Rights movement happened in the first place. It worked because it was sincere. I don't hear any sincerity today. Maybe that's why they all gave up having a message, and instead focused on their follower count. They don't care. If that's the game, sure, she's the queen of it.
Because there's nothing in her sound, her image, or her message that is lasting. Nothing special. Nothing that appears to be changing who we are, nothing that challenges who we've been. Nothing that changes how we see ourselves.
I suppose if I were to draw an analogy, one might say she is the Michael Bay of music popstars. The only difference is Bay is underappreciated for what he brings to the table, and people tend to hate on him. For whatever reason, Swift is overrated, and overappreciated.