Have fought this problem for years. Here are some other culprits.
Bad struts (yes, this can be a problem)
Severly warped rotors CAN cause a shimmy problem. Normally only felt under braking, can be felt at high speed if bad enough.
Incorrect air pressure.
T/C arm malfunction (missing hardware/nut at the end).
Faulty tires. I had tires that would balance fine, but produced a shake. After several attempts to have them balanced, I finally convinced the tire manufacturer they were bad. They replaced them, and the shake was gone. They were as amazed as I was.
Slightly imperfect rims, combined with slightly imperfect tires, combined with slightly bad rack bushings pushing slightly bad inner tie rod ends. Looked at individually, each of these may not be bad enough to cause the problem. Together they are a nightmare.
Tires that balance fine at 60, and somehow pick up a harmonic at 70 causing the shakes.
Seems our cars are very sensitive to vibration. Everything must be right to fix this issue.