Its not moot because going faster to chapel or keep gets you sooner the leap stone, thus shortcuting most of the castle, your right you still need to cover the map, yet, going the "normal" way (buying at library the relic and opening blue doors) is taking way longer.
Naked challenge (luck mode or not) is doable unassisted, many ppl did it.
The luck mode is only difficult is you stay low, but anything you beat up while been low will forcably get you lvl ups, so theres no real way around it. The exp gain system is made up to overpower you very quick.
In a tas anyway unless you seek speed boost, nothing will ever hit you at all. No boss are challenging, especially with frame precision, and will end up dieing very fast, naked or not, they basicly have all very low hp except in reverse castle.
I think challenge and speedrunning are not compatible for this game, i wish it was tho, but glitching is so extended and let you do so many things out of order that you could come up with any goals and still works.
If not using glitchs, i think the minimun is to have 3 relics + dracula ones, either leap stone or wolf(dive kick), mist, then bat or extended mist (with a tonnes of mp).
Edit: some exemple of arbitrary goals:
http://www.youtube.com/watch?v=18voV5lC6pI
http://www.youtube.com/watch?v=TvRUF_fxieQ
http://www.youtube.com/watch?v=8wFxLa9ivfk
While its not actually what you asked for, and severly use glitching, you can at least observ the game is uterly easy and theres nothing much "hard", all ennemys can be dodged or discarded.
If i came up with suchs goals its basicly because the overall difficulty is too low and not realy fun, while trying to go against the wind might proove to be more successfull in term of entertainment.
Heck see how
poor dracula can get owned by richter :p
I know some ppl would like to see a no glitch run, im not saying i dont "want" to do one, but im saying at least its not easy to make clear goals without the movie been extremly repeatitive or boring, now of course everybody have his mind on the matter, but well.
I know for sure theres not a single room in the game that is glitchless, its very hard not taking this in consideration.