Charles Cascarilla, a former Goldman Sachs analyst and hedge fund manager, believes he’s identified one such culprit: the Depositary Trust and Clearing Corporation, or DTCC, which is responsible for clearing stock trades. According to Cascarilla, the DTCC has done a woeful job of incorporating new technology that could speed up the stock clearing process.

“It’s like a 19th-century sewer system. It works till it doesn’t,” says Cascarilla, who claims the DTCC’s computer systems still rely on Cobol, an ancient programming language. (Fortune sent an inquiry to DTCC to verify this but has not yet heard back.)

For those not familiar, the DTCC is critical to the smooth operation of U.S. stock markets. The details of its operations can be mind-numbing, but in essence what the DTCC does is to act as a middleman to record every trade and provide a financial backstop to ensure those trades get settled.

Funded by banks and brokerages, the DTCC is a holding company that oversees various subsidiaries created in response to a record-keeping crisis in the 1970s. That crisis saw stock markets seize up as Wall Street choked on mounds of paper forms. The situation became so bad at one point that markets had to close every Wednesday to give brokerages and exchanges time to process stock certificates.

Moving things to computers has allowed markets to keep humming even as millions of retail investors have piled in through platforms like eTrade and Robinhood. The DTCC has also succeeded in speeding up operations, recently moving from “T+3” to “T+2″—stock market lingo that means the process for finalizing a trade now takes two days rather than three.

Such improvements are not good enough for the critics, who include Robinhood’s CEO, Vlad Tenev. On Tuesday, Tenev published a blog post that begins, “It’s time for T+2 to go.”

Tenev’s gripe is unsurprising given that the two-day lag in the clearing process is what forced Robinhood and other firms to restrict trading last week in stocks like GameStop and AMC. For the DTCC, such restrictions reduce the risk that a sudden tumble in share price during the two-day clearing process would leave brokerages unable to pay for the trades.

Brokerages choking off access to certain shares is a rare occurrence, and it comes in response to unusual market conditions—including last week’s short squeeze frenzies, or the manic investing that occurred in the 2000 dotcom bubble. But when such events do occur, retail investors become suspicious that the forces of Wall Street are rigged against them.

For Cascarilla, the situation is doubly frustrating because he believes his current company, Paxos, offers a solution. Backed by PayPal, Paxos has raised over $240 million to develop a clearing process that relies on blockchain technology rather than Cobol code. The company has received permission to deploy its technology in real-world trades and counts banking giants Credit Suisse and Societe Generale among its clients.

Cascarilla claims a Paxos-style clearing system means trades can settle in hours or even real time. He says this would free up capital by reducing the amount of collateral brokerages like Robinhood have to post with the DTCC. And it would provide a superior method for keeping track of who owns which shares—letting Wall Street avoid another debacle like the one that followed the collapse of trading giant Lehman Brothers in 2008. According to Cascarilla, Lehman’s ownership records remain a muddle to this day.

Not everyone is persuaded that Wall Street’s plumbing needs an overall, however. Larry Tabb, the head of market structure research at Bloomberg Intelligence, says the DTCC has done a “great job” in ensuring market stability while also streamlining the clearing process. In an interview with Fortune, Tabb pointed to the move from T3 to T2 as an enormous and successful undertaking.

Tabb added that proposals for real-time settlement are impractical because it would eliminate efficiencies that come with “netting”—waiting to collect batches of trades and then setting them off against each other—and as it would increase opportunities for inside information to leak.

And while everyone in the market might benefit from a faster clearing cycle, Tabb says the DTCC system is incredibly complex and that overhauling it would be time-consuming and expensive.

“Could we speed it up? Absolutely. Yeah, it would be better, but it would cost lots of money,” said Tabb, adding that he doesn’t view blockchain as a useful solution.

The DTCC, meanwhile, believes it is doing a sound job of the task assigned to it. A person close to the organization, who spoke on condition of anonymity, added that it welcomes companies like Paxos that offer market-based solutions.

“The DTCC would love to move to T1,” the person added, but said such a shift is not up to the DTCC alone, but would require permission from regulatory bodies like the SEC and FINRA.

Cascarilla, meanwhile, says Paxos’s clearing solutions will continue to gain traction as banks and clearinghouses discover its advantages. He added that Paxos is not calling for real-time settlement, even though that’s feasible, but instead for finalizing trades the same day or every few hours.

“We went from paper to centralized databases, and now it’s time to go to decentralized databases,” he said, using a term that describes blockchain technology.