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I, for one, think that the critical part is "how flexible is the note?" rather than being "in tune with itself".

"In tune" with what? Equal temprement? That just ensures that every note is equally out of tune.
Just intonation? The further one gets from the key of 'A', the more flexibility you need.

I would propose that the emphasis on "set it and forget it" has more to do with the larger number of people who feel that it takes too much work to go to that length of accuracy.

Dale,
Let's not forget that the intonation standards we have today are for the most part VERY different than the intonation standards in Berlioz's day. Plus, compared to the Awful-Clyde, the tuba probably was very in tune.