Ah. I don't have much classical music, so I tend to not have such problems with my tags.
> In the end it becomes a manual process as I feel obliged to manually verify each choice made by the tagger.
Though picard isn't an "auto tagger" (anymore at least) since it won't write tags without an explicit Ctrl-S to save the (selected) files. Newer picard versions show a diff of the tags in the bottom where you can manually fix things (it's not a full tag editor, so adding new tags isn't possible with it AFAICT), so detecting "picard did it wrong" should be fairly easy with it.
I would expect that simiar issues arise with things such as opera (as you point out), theater, broadway, national anthems, and so on. I guess "performance" pieces is a better name for this type of thing?