Well I agree completly with you on this part, but this logic doesn't apply to Yata Mirror and Totsuka Blade and will explain why below =D
Sasori created his weapons himself, especially puppets which were equipped with different types of weapons. That is true and In Sasori case I see puppets as extension of Sasori's power..., but only because he created them or just because they were his to begin with
Same with Tenten who uses normal shinobi weapons etc...
Not especially because as I said already. If weapon specialist posses normal weapons or is creator of these weapons himself, moreover weapon specialist has direct connection with weapon which would allows for example for weapon to be enhanced with chakra which could change properties of weapon, then Yes I agree that these weapons are extension of their power and they can't be meassured without them because weapons are part of them power.
For example:
Temari - She uses her fan and control with her barehands(has direct connection to it), better yet she could use her techniques with her fan and she could enhance her fan with wind chakra in direct combat...
Aburame clans - They use bugs as part of their power, because they cooperate with these bugs, giving themselves as bugs' home where they can live. Aburama clans have direct interaction with bugs, being able to control them and being able to influence these bugs chaning their properties If needed.
Ten Ten - She is weapon specialist, that why she can't be meassured without her weapons. All shurikens, swords and all other kinds of weapons she is able to summon and throw at enemy I could consider as part of her power.
However random shinobi with shuriken can't be meassured that shuriken is part of his power, because opponent can use his/her shuriken against that normal shinobi. In other words random Shinobi didn't summon or create these weapons, better he doesn't even control this weapon flying trajectory, just only throw it or protect himself/herself with it.
Okay, so explosive tags are the same I assume, since any shinobi can use it, and it's not part of special attributes.. What about the way Hanzo destroyed Nagato's legs? Or the way Konan "beat" Obito? Not part of their power? I know they made preparations to do it, yet it was combined with their jutsu.
My point is, that even if any shinobi can use it, say a random shinobi with shurinken, you wont measure that as part of his power, but fact is,
if he didn't have the shurinken, he would be weaker than if he had it!
Then comes examples like Kisame, who used shamehada, and even fused with it, but we clearly saw in the manga, that he took it from the big one (fugasaka or something like that =D).
So that ins't part of his power?
"So either tot/yata are the only exception in measuring wielders own power" - That exaclty my point, but this could more legendary weapons's case, If they existed... Now let's me explain why =D
Why Yata Mirror or Totsuka Blade(or any other legendary weapons. Sage of six paths treassured tools as well) can't be considered as part of wielder(Itachi) power:
[*] Yata Mirror and Totsuka Blade aren't Itachi to begin with , nor they are connected to Uchiha clan or Itachi's heritage
My example with Kisame still holds. Shamehada wasn't his to begin with, but he still found a way to combine it with his jutsu in a manner, that made him so much more powerful,
it has to be counted as part of his power! Itachi did the same, by combining tot/yata with Susanoo!
[*] Itachi didn't have direct contact with these sacred weapons, that why he can't summon these weapons whenever he wants. They can only be equipped with Sussano
This must just be an assumption? We really don't know enough about them, and in which manner, they are connected to his Susanoo, however, Japanese myth does indeed connect them to Susanoo! Susanoo used the sword of totsuka to slay some kind of 8 headed dragon, similar to when he killed Orochimaru. So the analogy is fairly clear in my eyes.
[*] Itachi can't change or set new properties ot these sacred weapons with inserting his chakra into them or modyfing them as Sasori could do with his weapons for example
Well this argument is hard to prove/disprove, but there is really no proof, whether he can or can't!
[*] These are legendary weapons which were found and equipped to Sussano, weren't part of Sussano to begin with
Yeah probably, but this should not matter in my eyes, because the fact that they can be combined with Susanoo,
and their size are made to fit Susanoo, along with the Jap myths and legends, I would not be suprised, if they were made for Susanoo!
[*] Yata Mirror and Totsuka blade could be used against Itachi because they are not his to begin with
I don't understand this argument? If Kankurou takes control of one of Sasori's puppets (despite modifying it), he could still use it against Sasori. The only difference is, that the creator would know the abilities of the weapons, but I can't see, how that should be relevant for this debate.
[*] Yata Mirror and Totsuka blade have constant abilities which can't be changed in any way
This as well, we don't know, because so far, we have only seen one person using them. If Sasuke obtains them, we might get to see more, but I doubt Itachi gave them to him.
They are too dangerous for that.
For me to consider weapons as part of wielder's power, they have to accomplish these rules:
[*] Weapons have to be created or used by wielder with his direct contact and direct control where to attack and what
I really dislike the first argument, because in my eyes, tot/yata are completely in direct control with Itachi, just through a different medium (susanoo), which is still controlled by Itachi. Also that they must be created with user, is kinda lame, as I stated much above. But of course the weapons need to function according the users will! That is indeed a major factor, and I agree on that. That is also why I said, I don't think Yata mirror will stop attacks, that Itachi can't see, or is unaware of.
[*] Wielder can alter, changes or set new attributes to weapons
[*] Wielder can enhance his weapon with his chakra to change it properties
I agree, if we can compliment it to more than chakra. Shinobi is not only chakra. Stamina, strength, tactics, etc. are also extremely important, when measuring ones power. Thus the way you use the weapon, can also be tactical. Like shurinken or explosive tags. Take Samurai for instance, clearly a Samurai is worthless without his sword, but with his sword, a guy like Mifune can match most top 20 - top 10 shinobi, if they fight close combat, since they wont be able to use hand seals.
[*] Weapon has to be part of their fighting style or his own abilities, not outside power as Yata and Totsuka
I disagree, that it's an outside power, because Itachi did indeed combine it with Susanoo? So I don't understand your point =D
[*] Legendary weapons which attributes can't be changed as well as can be handled by your own power doesn't use same logic of working as normal weapons
Well, we don't know this either. Surely they have some special effects given by them by so6p, cause he could create anything, and he probably created them for some special purpose.. If Sasuke got tot, it's clear that Madara is gonna be sealed by it. Then your theory is disproved =D but I doubt he got it :/
"but it still has to measure the enemies power
including their weapons, and skills with it" - I agree with, but only at conditions listed by me above... =D
I hope you now get my point
feel free to prove me being wrong. It was really nice and good debate
Got some of the points, some a bit unclear =D yet I think you are forgetting other important features, which measures shinobi strength, especially tactics. Weapons are important for tactics, and the better you are at using them, even if it's simple weapons, we have seen shikamaru using simply kunais to determine many fights, if he didn't have them, his overall strength had also been lowered (he probably had found another way, but the point is still valid =D).
btw, quoting those list like I did is rather problematic xD