Itachi takes this for many reasons.
For starters, Genjutsu is perfectly viable in this battle. Nagato does NOT have Genjutsu resistance. It's not on his profile to begin with, and is not supported by the series. To resist Tsukuyomi, you
need a Sharingan and a Kekkei Genkai, Nagato possesses neither. Itachi also has Ephemeral, which doesn't even require eye contact to begin with.
Interestingly, the Paths share the same field of vision, so if one falls for Tsukuyomi, there's a possibility that they all will, but I digress. This isn't necessary for Itachi to win this. Tsukuyomi only needs to claim one or two victims, and his other Jutsu will do the rest.
Amaterasu is literally the perfect counter for all the summons, and the Animal Path itself. He incapacitated the dog summon with it before, and even Nagato himself, who's far stronger than any of the Paths. Healthy Itachi would be able to use far more than when he was literally dying of a terminal illness, extremely fatigued from his battle with Sasuke, and nearing blindness. Even then he managed to spread it over a very large surface area, so targeting the Paths, especially when they usually stick together won't that difficult. The only two Paths who can do anything about it are the Deva and Preta Paths respectively, but even they can suffer some damage before dispersing it with ST or absorbing it. Since Itachi likely won't let the Naraka Path survive for long, the rest will be easy pickings from there. Amaterasu is impossible to avoid for them, especially in a speed equalized battle like this one, where Itachi's sharingan precog and enhanced sight will give him the edge in combat speed.
The Susano'o scales above all the Paths, AP wise, with the only technique in their possession that can potentially overpower it being Chibaku Tensei. The problem is that it's not in character for Pain to start with CT. It's a literal last resort that only comes up when he's completely cornered, and even then I think the battle will be over long before that ever happens.
Itachi can also attack and use his other Jutsu while he has his Susano'o activated, as we've seen in the fight against Nagato. He'll be throwing Shuriken and Katons around, and he'll also have access to his crows, genjustu, and Amaterasu to fall back on from within the safety of his Susano'o.
Of course I don't need to mention that the Totsuka Blade is a one-shot once it lands, and there's nothing they can really do about it. He can fire it off from quite a fair distance away as he did against both Orochimaru and Nagato. Itachi always uses it when his opponents are off-guard, too, to minimize their chances of escape. So he'll wait until he creates an opening before using it. His Yasaka Magatama are also capable of one-shotting any of the paths, and he can fire them off from a safe distance to have the maximum effect.
His intelligence will allow him to figure out most of Pain's abilities in mere minutes, as he's done as an Edo Tensei. His analytical skills are second to none, and will ensure that he spots openings to exploit. He doesn't fire off his Jutsu haphazardly, and will only use them when he knows they have a higher chance of landing. He's not stupid, and won't waste chakra.
Finally, I'd like to point out that Itachi's stamina is not nearly as bad as people seem to think. His battle with Sasuke perfectly highlights this:
- He first had a sparring match with Kisame.
- Then had a genjutsu battle with Sasuke.
- Then used Tsukuyomi.
- Then had a Taijustu battle, before they exchanged several Jutsu.
- Then he used Amaterasu and covered an absolutely massive area with it. Easily hundreds of meters.
- He then activated Susano'o to survive Kirin.
- Then activated it again in order to seal away Hydra Orochimaru.
I genuinely don't understand how you can look at all that and say he has terrible stamina. Keep in mind that, again, he was dying from his illness and likely in great pain the whole time, he was suffering from the after effects of using the Mangekyo and was nearly blind, he was drained from firing off so many Jutsu that require a lot of chakra, and he was fatigued and injured from the battle. Obviously a healthy, fresh, Itachi won't have nearly as many disadvantages, so his stamina will hold up just fine.