I've only had one tech, now retired, that I trusted not to do really stupid things, especially after being told expressly to not do those things. One thing that drives me bonkers is long neck corks, especially sanded to a taper. I show them the existing cork and say 'Don't make it longer than this' and they do anyway. I don't trust them with my mouthpiece to size the cork unless I prepare it first so WHEN THEY DROP IT I don't lose $1600. The last guy that worked on my MK VI tenor gave it back to me with large, serious dents along the body in the open area between the palm keys and pants guard. I about passed out. He swore I gave it to him like that - I was speechless. Fortunately I knew a great dent guy who fixed it for $20 and you cannot tell anything ever happened. I had also told this guy 'Do not use any abrasive material or tool anywhere on this sax without express approval.' guess what - he proudly told me that he had 'leveled' the tone holes because 'he had to'. He also sanded the neck during cork replacement which is why he put on the long cork - to cover it. I have been plaqued with incompetence like that my whole life. I took my alto to a local place (with their own storefront and lots of work) for a pad job and they basically destroyed the sax. They did something when they polished the keys (after being told 'no buffing') that left strange gouges in the lacquer. I could not for the life of me figure out how/why they did such a thing, plus everything else they did was awful. Another time the place I had trusted in years past no longer had a woodwind guy so they were sending their work to another shop 70 miles away. I went to that shop with my Martin baritone to get it washed, some dents out, the upper loop brace re-soldered and a few pads here and there. I agreed to the price and left the horn. After picking it up, weird things started happening and when I sat down with it to take a look, I found all kinds of crazy cork placements, loose screws, etc. I had to take it apart and re-do the set-up myself.
So I really have to say if the sax is not worth paying the high prices of the 'elite' shops, sell it and get a new one. I believe 90% of saxes existing in America have profound issues induced by incompetent repairs, either by owners, others or 'certified' techs (NAPBIRT). These guys I mentioned were all NAPBIRT. When I see that sign, I run the other way.
Oh, I forgot a good one (there have been so many incidents) - the guy that dented the MK VI also worked on my Selmer USA alto, which he did first. The pants guard on this horn screws directly onto the two posts for it rather than slipping into a slot in the ball of each post like the MK VI. So, when he assembled the MK VI, even after taking it apart himself, he stupidly did the same thing, rather than putting the guard in the slot and then tightening the screws. A small matter, you say? Okay, when he tightened the screws he closed the little gaps by over-bending the brass, setting them up to break off at some future time. I was actually surprised that they didn't break when I corrected what he did. So imagine having to find these posts and them having them soldered on, destroying precious remaining lacquer on a valuable horn - that's why it bothered me. Oh, I forgot to mention how I found that particular problem - naturally, I had to tear the whole horn down and fix stupid things he had done to it, so that's when I found the clothes guard problem. Why did I go to this guy? Well, I had known him a long time and knew that he worked on saxes around town and I never heard anything bad about him, so I took a chance. Bad move.
I think this is a sufficient response to the question although if I really were to think about it, I could relate many more examples. If I have to take a sax somewhere, if it can still be played when I get it back and it has not suffered significant damage/value reduction, I consider myself fortunate.
But there is hope; I recently took saxes to the local Music & Arts which has full-time techs now, just to get some necks sized-up. The guy did a great job and was very thoughtful in what he did. Now I'll try him out on some dents and pads, etc. to see how it goes - this might be a really good thing.