RE contemporary H&H Regulation
Barrel convergence is built in by machining the breeches to predetermined angles, and careful assembly of the tubes assures it during the barrelmaking process. H&H's barrelmakers are arguably the best in the business, and nowadays they have certainly trained most of the best working for the trade at large: Higgins, Blacker, the Frenchman who works for Hartmann & Weiss, et al.
All the fixed chokes are hand regulated for pattern by counting percentages and tweaking as needed. Steven Cranston, H&H's dedicated regulator, certainly checks for POI, as when he is plating a gun he shoots at a mark on the plate. A gun should not have any major POI issues by the time it gets to him, however. It was my impression that barrels would be "scrapped" early on if they exhibited major convergence problems, or it was thought they would.
If a bought-in boxlock at H&H was badged "shot & regulated by H&H" in the old days rest assured it was. The company built its reputation on rifle regulation and has always taken pride in its regulation at large. It's part of the H&H mystique, and was no doubt part of the reason the H&H salesman could 'justify' selling its boxlocks for more.
Robin Brown, at AA Brown's, still hand regulates and so will David McKay Brown. Many others in Britain, however, no longer do, though I feel certain they ck for basic POI.
As to the question about how widely this was practiced historically on an average gun: certainly it was ubiquitous with best guns in the UK, and widely done on the better sort of mid-grade gun. Was every gun so checked? Jack Rowe would know.
I don't know enough about the American practices to even guess but those researchers who have gotten first-hand looks at the record books could probably tell you. You may want to try the question at one of the dedicated sites to a particular American gun.