It depends on whether Jerry Jones the owner would self-constrain himself to his Jimmy Johnson era version. It is what older fans have a less clear memory of him, while younger fans have zero recollection of him as.
'Would Jones do it?' is the question? The answer is that it is possible since he did it before (the Parcells' version does not really count since he used the stadium pitch as an ulterior motive).
Changing management is not a phenomenon restricted outside the NFL. It commonly happens in any form of business. It may be strange to some members but it happens in the NFL too.
New management is not some magic pill though. A general manager could oversee similar results Jones achieved. They could also run football operations worse than Jones has. Some will dispute that last possibility but it is true nonetheless.
That said, a new, qualified general manager can instill new vision and innovation. Hiring, drafting and acquisition decisions would be organized through a different lens. This is the choice Jones has not only deprived his fans for reaching higher heights for his franchise but also cheated himself as its owner.