Ever since news of its precarious tilt became public in 2016, San Francisco’s Millennium Tower has mortified its owners and entertained just about everyone else.

Add such twists as last week’s oddly cracked window on the 36th floor, caused by who knows what, and the saga shows no signs of ending anytime soon. It also shows, I hate to admit, that architecture can be irrelevant in terms of a building’s renown.

For instance: When people now visit from out of town, our sinking glass shaft is the 21st century sight they want to see. Museums by name-brand architects are a badge of civic pride, but let’s get real: Millennium Tower is more fun to ponder over drinks.

This isn’t a criticism of the 645-foot high-rise at Mission and Fremont streets, which opened in 2009. I also don’t want to minimize the strain on the owners of the 419 condominiums: It can’t be fun to know your 58-story home has sunk about 18 inches and tilted 14 inches to the west.

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But in weird yet undeniable ways, Millennium Tower has come to symbolize the hubris and fragility of today’s San Francisco — and how buildings only capture the public’s imagination when they tap a nerve that goes beyond aesthetics.

In this case, obviously, there’s the “what were they thinking” when they erected a massive tower of heavy concrete without locking it to the bedrock. In earthquake-vulnerable San Francisco. On landfill, no less.

And who are the people at risk? Residents wealthy enough to desire and afford an address that billed itself in its original marketing as “a shimmering reflection of the city that inspired it ... we’ve elevated living well to an art form.” Even now, a two-bedroom on the 34th floor is listed at $2.2 million.

If this were an office building, the schadenfreude wouldn’t be nearly so ... rich.

Nor would there be the same local buzz if the crystalline high-rise were lost within a thicket of sky-nuzzling slabs or off the beaten track.

Think again. This is the epicenter of the “new” San Francisco, for better or worse, defined by tech behemoths and a globalized sheen. Towers adorned with Salesforce logos frame the intersection’s other three corners. The plaza for Salesforce Tower allows a full frontal view of Millennium Tower, bottom to top.

Two new towers leased to Facebook loom to the south and east. Closer still is the city’s new transit center with its rooftop park — an ideal vantage point for strollers to stop, point, and try to discern whether or not they can glean the lean.

Yes, these all are caricatures to some extent. Several other nearby towers of recent vintage don’t go down to bedrock, either. The difference? They were engineered correctly.

What counts is that the caricatures feel right. Details aside, they resonate.

This is important, because resonance is the sensation that make certain buildings seem larger than life.

In the Bay Area, it’s why the Ferry Building has a prominence far beyond its actual dimensions. The 245-foot campanile flanked by classical arches evokes the ceremonial air of a proud peninsular city at the dawn of the 20th century, welcoming the world with an assurance that outsiders would want to find their way here.

The Transamerica Pyramid strikes a similar chord — a steep concrete triangle that’s not great architecture but is instantly recognizable. Something you’ll find nowhere else, as idiosyncratic as the neighborhoods around it. No wonder people hated the idea. No wonder it’s now a fixture of postcards and local lore.

Millennium Tower isn’t nearly as memorable visually, to be sure. The diagonal shot of aluminum fins across milky blue glass gives a kinetic charge to Handel Architects’ sculpted high-rise. Otherwise, it would blur into all the other glass towers that have popped up in the past decade.

But the man-bites-dog notoriety knows no boundaries: What began as a development project becomes a metaphorical comeuppance for the 1 percent. That’s why there was a much-publicized feature last fall on “60 Minutes,” and feature articles in publications, including the Toronto Star, England’s Daily Mail, Forbes and the South China Morning Post.

Here’s an example drawn from personal experience.

Last year I was on the East Coast and had a glass of wine with the dean of a prominent school of architecture. The dean asked me about just one San Francisco building. Guess which one.

With time, presumably, Millennium Tower’s prolonged moment in the spotlight will pass. The cracked window will be replaced. The tower will be straightened or stabilized. A small army of contractors and attorneys will find new sources of lucrative fees.

Italy’s Leaning Tower of Pisa once again will be in a class by itself.

Until then?

In the lavish marketing brochure from 2009, the developers made this promise: “Millennium Tower is destined to become an icon.”

They were right — but not in the way that anyone back then could have predicted.

John King is The San Francisco Chronicle’s urban design critic. Email: jking@sfchronicle.com Twitter: @johnkingsfchron