Equipment restrictions are part of your character. To compare apples with apples, consider a Fighter versus a Barbarian. Barbarians have more special abilities, including some physical damage resistance at high levels. Fighters, on the other hand, can wear heavy armor and achieve grandmastery (rather than mere specialization). An unarmored Fighter with bare fists loses all but two class benefits: great hit points and saving throws (at high levels, anyway). Even non-magical gear turns such a waste of space into a force to be reckoned with. Also, bare fists being nonlethal stops warriors cold.
IMO the point of a poverty challenge is you can't use all the fancy toys and, perhaps more importantly, powerful expendables (potions &c). Banning even basic equipment turns it into a Spells-and-Monks challenge. Banning magical gear (which covers potions, scrolls, and such) would be enough of a challenge, especially since so many monsters are entirely immune to normal weapons. My proposed mod would fix that last point without giving you the hit/damage and other benefits normally associated with magical weapons (since the game engine stores the enchantment level, to-hit bonus, and damage bonus as separate variables).
As for allowing temples, there are several mandatory encounters with level-draining creatures. Without scrolls, most classes would force you to save/reload until you survive without taking a hit. I don't think the point of a challenge is "reload until the RNG gives you perfect rolls".
Of course, if this were NWN (or maybe IWD2), a no-items challenge would be possible, if still damned hard, for most classes.
The challenge isn't possible for pretty much every clase (with enough save scumming a monk might be able to do it, otherwise only sorcerer).
It's impossible for warriors, its (essentially) impossible for thiefs, its (essentially) impossible for clerics/druids, impossible for paladins, barbarians, and (if you count reading scrolls) non sorcerer mages.
If you use items (excluding quest items), then it's not a no-item run. If you use money (except where you need them to advance in the plot), then it's not a poverty run. If you ever change the difficulty from insane, then it's not a insane run. It's as simple as that.
If you say "but my warrior needs a weapon and armor to win", well then he could play a insane solo poverty run.
If you say "but my monk needs to use the temple to restore levels to win", then he could play a insane solo no-item run.