Jack Welch’s CEO factory has stopped production: Good riddance.

It’s not just Crotonville that’s a tough sell these days for GE. It’s also the executives the training centre helped shape and the leadership philosophy it long espoused. A GE pedigree was once highly coveted by corporate boards looking to fill out their companies’ C-suites. But now, GE-bred CEOs are developing a very different sort of reputation—that of flameouts rather than stars. For the ur-example, look no further than The Boeing Company, where three of the last four chief executives all hailed from the once powerful conglomerate. “The running joke around the company is whatever you do, don’t hire another CEO from GE!" one current Boeing manager quipped to Fortune earlier this month.

It’s a damning indictment of the house that Jack Welch built.

Welch ran the place for two decades, a period in which he developed a management system that rotated high-potential executives through different parts of the sprawling enterprise—a few years here with the now-infamous financial services division, a few there with plastics. Ultimately, that meant mastering the “GE way" was deemed more critical to running a successful business than developing deep domain expertise. To the outside world, it gave the impression that a GE-trained executive could parachute in and expertly lead any business, which is how Crotonville graduates ended up in charge of companies like Albertsons, The Home Depot and Intuit that have seemingly little resemblance to GE.

The Boeing fiasco is just the latest proof point that it’s time to abandon the premise of interchangeable CEOs, who are produced at a GE-like CEO factory and can be swapped in and out like widgets. The world is too complicated, the job of a CEO today too challenging and the products many companies produce too technical for this model to work anymore—if it ever did.

At Crotonville, GE reinforced the top-down, corporate-knows-best mentality that has gotten a crop of its alumni into trouble. Executives would disappear for a few weeks at a time to the bucolic campus and learn all about Six Sigma quality and cost cutting in a way that, in retrospect, seems alarmingly divorced from the realities of what was happening on the shop floor. Now we can see how that mentality played out at a place like Boeing: Engineers were sounding the alarm on the company’s safety issues as far back as 2001. But apparently its executives just couldn’t hear the warnings in Chicago, where that same year Boeing relocated its headquarters far from its Seattle production lines.

Compare that to the lean manufacturing philosophy that Larry Culp has put in place at the dramatically slimmed down GE. In this world-view, answers to problems can be found on the factory floor, which is also where the culture should be shaped—not at some far-removed corporate command post. Executives should be spending their time with operations, not in Crotonville-like Ivory Towers or wood-panelled conference rooms. There’s still a benefit that comes with an academic leadership program that lets people refresh their thinking and opens them up to new ideas. But as Culp has proven, it needs to be more in balance with what a company actually does and how it operates.

GE may no longer be considered a CEO factory, but some corners of corporate America seem to still be searching for one elsewhere. Increasingly, headhunters and boardrooms are looking for their next CEOs to have Amazon on their resumes. It’s the GE of its day, with its vast operations and legendary management and growth. But already we have a few case studies—Dave Clark at Flexport and Matt Furlong at GameStop, to name just two— that yet again demonstrate that the CEO factory model is too simplistic for today’s fast-changing world.

The discourse swirling around who should be the next CEO of Boeing suggests that the message might finally have gotten through: The company needs to prioritize manufacturing experience rather than nebulous ‘leadership skills.’ That’s going to require hiring for very specific expertise, not just someone who ticks the boxes of what a CEO should act and look like.

It’s a smart way of thinking about all CEO searches, and especially the complex ones. Boeing’s next chief executive must be able to rebuild the company’s culture and turnaround the business—all while handling an incensed public and Washington. That kind of executive is made to order, not one likely to be found rolling off the line of any CEO factory. ©bloomberg