There is no knife that is more dangerous than a modern handgun; to the contrary, knives are much less dangerous.
I'm certainly no authority, nor do I have a clear idea how to measure dangerousness; that said, I've met more than one or two cops and martial artists who'd tell you only fools are less wary of knives in criminal hands than guns.
Knives are certainly very effective weapons in trained hands, and dangerous weapons in nearly anyone’s hands.
Your statement clearly is a corollary of the statement that the person is the dangerous part of the equation.
Still, I think few would argue that knives are generally less dangerous to the public than handguns are. They are much less likely to cause damage to unintended targets, they generally will not be able to penetrate walls and windows to effect damage, and they are generally ineffective beyond arms length (in spite of what a few highly trained experts can do under ideal conditions).
While handguns have utility outside of self defense, knives have more. While handguns are common, knives are more common. While handguns have improved technologically beyond those in common use when the Constitution was written, knives have changed little.
Ballistic knives are some of the most deadly. I’d hope they’re going to lift restrictions on those.