Will the exchange still exist? Will it be a museum? An office complex? An automated emporium run by robots?
Nobody seems quite sure, though the building itself does maintain its nostalgic appeal even if it's lost much of its relevance as a trading center.
"Symbols matter," said Nicholas Colas, chief market strategist at New York-based brokerage Convergex. "It's important to have a symbol that people can relate to, and it's much easier to relate to a physical space. It will be important for the New York Stock Exchange to maintain some relevance with investors."
As things stand, the prospects for the building and what happens inside it hinge on three things: Just how far the trading community pushes automation, how hard regulators push back, and how well the 80 or so locations now where stocks are traded can maintain their trust and credibility with the investing public.
Read MoreCramer: NYSE halt shows its lost importance
Automated trading has taken up about four-fifths of the stock market's volume. Dark pools—privately run trading centers away from the NYSE—are scattered around the metropolitan area. Exchanges around the world such as those in Tokyo, London and Shanghai are seeing their volumes increase, though they still draw just a fraction of the volume seen in New York at the NYSE and the Nasdaq.
The current market is dealing with one whale of a black eye caused by suspicion over high-frequency trading and its stranglehold on market activity. Incidents like Wednesday's trading shutdown and the Nasdaq "flash freeze" nearly two years ago add to the market's sullied reputation.
The proliferation of trading aberrations such as 2010's "flash crash" and the intense debate over Michael Lewis' HFT-centered book "Flash Boys" has underscored the credibility problem, which will have to be rectified—and soon—if the NYSE is to have a future.
Conversations with the folks who help make the market machinery work reveal some interesting—and surprising—thought trends.
For instance, there is a pervasive belief that the market will become less fractured and perhaps even a bit slower than the current incomprehensible millisecond-moving speeds. While automation is a fact of life, there is no widely shared dystopian view of a market run by faceless machines without accountability.
"We're moving faster and faster. The speeds are incredible, but we're going to get to the point where it doesn't go any faster," said Peter Costa, president of Empire Executions and an NYSE governor with 34 years of trading experience.
For the NYSE and its physical future as a relevant part of market structure, the battle essentially comes down to humans versus computers. While the machines have been gaining more and more ground, market veterans hope the humans continue to be part of the equation.
"You like to have someone involved. The investor relations officer, the chief financial officer, really has no idea what's going on in their stock," said Joe Saluzzi, also a principal at Themis. "There are no specialists involved. They need more information as to what's going on. It's not there anymore."
While the amount of bodies on the exchange floor indeed has dimmed considerably over the years, the level of employment in financial services has remained fairly and surprisingly resilient.
Read MoreWhy it took so long for the NYSE to reopen
Financial services jobs peaked out in late 2006 at about 8.4 million, according to the Bureau of Labor Statistics. However, a continued move higher has the total back almost to its precrisis levels, with 8.13 million working in field as of June.
So where does that leave the exchange as a physical property?
If you close your eyes tightly enough you can almost see the tumbleweeds rolling across the cobblestones past the Wall Street subway station, past the Deutsche Bank building and gliding on a path to nowhere. After all, what possible use could there be for such a structure in the next age of trading?
"I don't think the NYSE exists anymore period," said Dick Bove, the outspoken banking analyst and vice president of equity research at Rafferty Capital Markets.
Bove sees the global financial center shifting from New York to various other places around the world—Canada, China, wherever countries are committed to a thriving banking sector and not obsessed with handcuffing "too big to fail" institutions.
Other challenges New York faces include its inability to attract technology-focused industries, intensified regulation from city and state politicians, and the rise of financial centers around the world that will provide major competition.
All those factors, he said, will make the NYSE, if not obsolete, at least substantially declining in relevance.
"It's a historical oddity. It should be given to one of the historical preservation societies," Bove added. "It does not exist today. It will not exist in 25 years."
—Portions of this story appeared in an earlier report.