Last year I sent a vintage American gun of excellent quality to a good barrel man to have the chokes opened up. But out of curiosity I also asked him to pattern it before, during and after "regulating". He called one day and began by saying "these barrels must have been joined on a Monday by someone who had a bad weekend". He went on with describing how one barrel shot to POI but the right shot about six inches out at 16 yards! He did ask if I wanted it fixed cause as is the gun gave me plenty of excuses for my frequent misses. Feeling I had enough other ways to explain away my misses I told him to go ahead. Well, with a lot of reaming, polishing and patterning he brought them to the same POI. fortunately the muzzles had a lot of metal to work with. Point of this post is that even one of the premier makers did not take time to fine tune where they shot.
Incidentally, shop rates at the pattern board were enough to buy many flats of ammunition.
I intentionally left off the maker so this thread wouldn't turn into a spitting match. But they were good.
And old friend of mine, a gunsmith, had a pretty serious trap shooter for a neighbor. Chuck told me about tinkering with the choke on the trap gun, making it slightly eccentric, in order to move the pattern. (Might well have been a double, probably an OU, but can't recall for sure.) Time consuming, but per the above, it can be done. But while I don't claim to have looked at nearly as many patterns as someone like Bob Brister, the ones I have shot pretty much tell me that most sxs--even relatively inexpensive ones--aren't off a great deal when it comes to shooting to point of aim. I can only recall one example that was really bad. Close to as bad as the one in Joe's post.