I thought you meant it funny - my apologies if you did not. As for the "your arbitrary rule that the root of a dim7 chord MUST lead", if you were addressing me personally, I wrote the very contrary.

My bass note naming scheme is indeed not reflecting any harmonic role. In cases where such a role is clearly visible, it should take precedence. In all other cases any rule will do. Mine has the advantage of easy readability, not requiring a slash for the bass note.

The applicability of "functional harmonics" diminishes continuously, starting about 1800 and not quite ending with Stravinsky (as suggested in the other thread currently active). Whenever it fails to explain something in a way that benefits the musicians, these should not be bothered with it at all. Note that other theories, "non-functional", have been suggested, e.g. by Paul Hindemith, principally targeted at composers. Those who read those books at all rarely found them of use for their own work.

Jazz theory may be an exception, but has also often been criticized. For the question of the thread title, its most common answer is "all are equivalent". Since the authors define the chord by towering thirds, it makes sense to use a name for which this does not imply any double accidentals, but I would not worry too much about that. Jazz and orthography are separate worlds anyway.