There has been plenty of research on shimmy on motorcycles. You can find videos of "tank slappers." They generally don't consider stiffness at all, but the one (simulation based) paper I read that did said they had to reduce frame stiffness to a ridiculous level before it contributed.
The thing that nobody seems to be able to explain is why a frame would bend back and forth when there is a hinge in the middle that can't support bending moments at all in the direction of shimmy. And we had some undergrads do some modal testing of bike frames, and even the biggest, wimpiest vintage road frames had a 1st natural frequency above 10 hz. That's faster than shimmy. It was in the rear triangle, btw, and I don't think anyone asserts that shimmy is related to rear triangle stiffness. This actually proves that shimmy isn't related to frame stiffness, but people don't understand vibration and dynamic systems. So it's not surprising that nobody understands that. This includes ME undergrads, who have to take a vibration class and associated lab. Like I said above, I just let it slide most of the time when I see someone mention it nowadays. The cycling community believes all sorts of happy ********* and there really is no combatting it.
My belief is the reason this is so widespread is that it does look like your top tube is bending. It's so much that you would definitely die if it bent that much. It's an optical illusion.