Steering wheel shimmy

I have a 2005 Subaru Legacy and the steering wheel shimmies all the time. My Subaru mechanic can’t find a reason for this. I did try another general mechanic, without telling him that this appointment was really a ‘second opinion’ and after rotating all the tires, numerous test drives he couldn’t figure it out either and referred me to my original mechanic, telling me that he’s the best Subaru guy in town.
Any suggestions anyone?

hmm … Assuming all the obvious visual inspections and simple-to-do tests of the steering and suspension parts have been done. And that the tires are exactly the same size that came with the vehicle new. And the alignment and wheel balance on all 4 wheels has been verified. hmm … well, to totally eliminate the tires, you could purchase two new front tires of a different brand I suppose, see if that makes a difference. If it didn’t, you could just store the two extra tires until you need them. I’m suspecting a tire problem of some kind.

Did they both check the alignment and the articulated joints for wear? How old are the struts?

Did either of them check the balance of the wheels on a machine that does “rebalancing”? Road force balancing simulates the rolling forces by pressing a spinning disc against the tire’s tread while spinning it. That can detect anomalies that regular balancing cannot. Post back.

If the problem is not related to tires (broken belt, balance, etc) then here some possibilities.
Alignment.
Worn suspension or steering component.
Sticking brake caliper piston or slide.
Worn CV joint. These can be a problem even without torn boots or clicking/knocking noises and sometimes there is no way of really checking these unless they’re removed from the car. Of course that brings up the scenario of if they’re out anyway then replacement is the better option; even if the option is a bit distasteful.

Try an independent alignment shop. Fixing a shimmy is their thing.

A bad axle/CV joint can cause vibration/shimmy as OK4550 said. If the shimmy is proportional to the rotational speed of the wheel that would be my first guess.