Any mechanic is capable, but the key is their experience and what procedure they use. Its not really a technical task per say, just takes patience and to follow the complete process with no shortcuts.
However, all proper rigging starts with a control system that meets spec: wear within limits, clean, and lubed. If your system is not to spec, then usually the results will not be spec either.
A good place to start is at your next annual when everything is open and review, clean, and lube every flight control item per the book. Or if this is something you want done sooner, then open things up and check it. Once you know the system is to spec, then have it rigged per the book.
What's your current mechanic input on this?
If you have access to your specific maintenance manual, perhaps read up on it to give you a better understanding on it. Any questions post here?
"Any mechanic is capable"...... I have doubts of that based on my experience flying rental aircraft.....
that said I do understand that it's likely more a result of a lack of desire from the owners to have it done...
Still, I'd venture to guess that they all "should be" but many aren't
thinking this through and based on comments here, I'd guess that many/most aircraft flying are mis-rigged as a result of partial efforts and band-aid tweaks by well-intentioned A&P's
I've seen things like this in many areas though my career as a mechanical engineer (non-aviation stuff).
The example that comes to my mind often is lug nuts on a car. Most folks would say that any mechanic could properly change a tire, right?
I grew up turning wrenches. Small engines, small appliance repair, cars, tractors, etc... reading and following maintenance manuals for torque specs, etc... I knew how to change a tire. Later I went to college for a drafting and design degree, followed by a Mech E degree. Took extra courses in machine design which included threaded fastener stuff, etc... I knew how to "properly size and design" a threaded fastener system. My first job out of college had me doing some work with threaded fastener inspection, NDT work, and such
OK, I knew a little something about changing a tire.
A couple years after school I sat through a day-long threaded fastener course at work. It was put on by some engineers from the company that supplied threaded fasteners to the paper mill I worked for. The class was targeted at our millwrights and other maintenance folks. My eyes were opened to the concept of "you don't know what you don't know". I was blown away by how much I did not know about properly torquing a lug nut!
it seems like a "done correctly" rigging job would be a very involved thing. A whole-aircraft alignment restoration in a way...
it would need to START with inspection/replacement of things like engine mounts and panel mounts, frames, etc.
probably followed (or maybe preceded by) inspection of proper structural alignment (wing washout and positioning, fuse and spar damage/twist, etc..)
then followed by a very methodical point-to-point adjustment based on type.. such as flap, then ailerons, then... in a specific order, not out of order.