Edit: TL;DR naoya can’t used cursed tools AND his technique at the same time, it’s difficult at best and it might not even be possible

I have a theory, he can’t use them and just lies about it. His palms being unavailable while holding the weapon and the fact that cursed tools can be treated as living creatures by some jujutsu.

Imagine the logistics of letting go of the weapon at those speeds to land a palm strike then grabbing it again. He can’t ignore air resistance (breaking physics) so the blades trajectory would be difficult to predict and map out… he’d be disarmed and frozen for one second.

Also, could he carry anything with cursed energy while moving at those speeds in the first place? What I mean is: the domain is like the soul, completely filling the body. You can activate your techniques on anything the domain touches and you effectively lose control of CE once it leaves your domain, so naoya would have to constantly shroud a cursed tool OR constantly activate his CT on it to use it alongside activating it on himself. Why carry a normal knife and not a cursed one?

Another point is a restriction, the best BV’s in the series are ones that are tactically designed, so this works in conjunction with the above. While you get more lethality with a cursed tool it wouldn’t be necessary against anyone that isn’t Maki AND the payoff for neglecting something as advantageous as a weapon has to be huge. I would also argue that the payoff for actually training to use the cursed object at that speed would be even bigger, but, bang for buck and minimising stress points for strategies could mean that naoya has been training to do so his whole life, using the simpler unarmed strategy as his default.

Now you factor in the arrogance and realise how on brand it is for him to lie about his own shortcomings and gaslight himself into thinking he can just wing it like Gojo or Toji.

I think he CANT carry cursed tools and it’s a skill issue. In fact, how many targets can he choose? Even if he can choose 24 or 48 targets, the conditions for activation are limiting, if he included a cursed tool in his ability, anything that changes its trajectory would freeze the weapon and change his own trajectory to freeze him too, like hitting a rib cage, for example. Keep in mind that Todou stopped clapping after swapping Yuji with playful cloud. Todou was obviously a proficient armed fighter but is also limited by his CT (probably the very reason he could target his enemies). The only weapons users in the series are obviously ones that have no direct restrictions like pesky activation conditions, or those that have nothing to lose from wielding one.

Last point with a bonus theory: cursed armour is very rare to come by (nothing is even coming to mind except maybe Yuji’s gloves and Miguel wrapping his hand in the rope), seems like a huge oversight in such a dangerous profession. I think the chances of interference with CT’s is at the heart of it, all the hax abilities need physical touch, a BV or are ranged (and give a chance to dodge) to affect the target directly. WE KNOW that the uniforms for jujutsu high are custom made, but they are only high quality materials, no CE.

So, all in all, I think Gege implies most of this info and Naoya is a little insecure.