Robo-advisors’ time has come -- and it may have gone.

That’s the gist of a new white paper from New York-based Silver Lane Advisors, titled “Have Roboadvisors Jumped the Shark?”

When a television series “jumps the shark,” it reaches a point of saturation and episodes hinge on increasingly bizarre plot devices, no longer concentrating on the character relationships that made them initially popular. “Jumping the shark” now generally refers to the inevitable decline in something’s quality and relevance.

In the same way, Silver Lane argues that some of the media hype surrounding robo-advisors borders on ridiculous, and if independent robo-advisors don’t adjust to a changing marketplace, they will find themselves eclipsed by traditional financial firms.

The analysis compares robo-advisors to the online banking movement of the 1990s.

Starting in 1994, a number of online-only banks attracted a small rush of early adopters, creating a tech-driven start-up craze.

Over time, large, traditional brick-and-mortar banks recognized the utility of online banking and began to flood the market with their own online portals.

“Once Bank of America threw its weight behind its own online banking product, it was adding more accounts every 90 days than [Internet-only banks] did in five years,” writes Silver Lane.

The relatively new Internet-only banks couldn’t compete with the well-established industry mega-brands, and within a few years most of them folded.

“While online account access took off in the 1990s and 2000s, it wasn’t Internet-only banks that survived but rather the online banking offerings of existing banks. Internet-only advisors are likely to be the exception, not the rule,” writes Silver Lane. “Going forward, it is our view that most customers will look to the Internet as just an additional delivery channel to complement the way they currently access their investment accounts, much like they already use online banking.”

Like Internet banks, robo-advisors will find a niche and create a lasting legacy, argues Silver Lane, but independent enterprises like Betterment and Wealthfront may not disrupt traditional financial firms.

With the attention of traditional advisors like Schwab and Vanguard, which have developed their own robo-advisors, and BlackRock and Northwestern Mutual, which have entered the market through acquisitions, the focus on independent robo-advisory firms will fade.

To maintain their market share, independents will be pressured to spend more on marketing and to provide more human services, but lack the economies of scale to compete with the Schwabs and Vanguards of the world, Silver Lane predicts. That may be why firms like Betterment, which recently announced it will begin offering 401(k) plans for small businesses, appear to be pivoting toward the business-to-business market.

Investors will likely demand that their traditional advisors provide some of the automation and streamlined digital interface of robo-advisors, but will still want their own advisor, writes Silver Lane, “Today’s consumer wants eAdvice, not an eAdvisor, just as yesterday’s wanted online banking, not an Internet bank.”

This means advisors have an opportunity to adopt digital advice tools to efficiently serve a larger segment of investors.

“Our sense is that traditional advisors who wish to combat the robo-advisor wave are more likely to create a new, low-touch automated service offering as a complement to their existing books of business. One study estimates that 8% of top advisory firms currently offer some sort of robo-advice, with another 20% planning to do so within the next 12 to 24 months.”

And robo-advising technology is likely to survive well into the future, but not necessarily on the business-to-consumer level.

“Internet-only banks generally did not survive, but technology companies that enabled traditional banks to get into online banking thrived,” writes Silver Lane. “The same principle applies here. Our sense is that advising the advisor will be a better stand-alone business than advising the unadvised.”

Silver Lane predicts that other traditional fund-issuing firms, like State Street and Invesco, will be the next big players in the online advice industry, and that independent robo-advisors playing at becoming disrupters may actually find themselves losing steam and jumping the shark toward irrelevance.