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Kakashi is probably just unlucky and has an inferior sharingan that doesn't interface well with his body. Practically, we've seen that almost all of the sharingan abilities manifested almost by themselves. Perhaps Itachi had to develop stuff and perhaps not.
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Sasuke seems to have learned to use the amaterasu fairly easily and almost unintentionally.
Sasuke has indeed learned to use Amaterasu with enough ease, but we have no idea what Itachi did to him. Another problem is the sharingan's ability to copy jutsus. Sasuke has the mangekyou and he's seen a jutsu that the mangekyou can use, several times. We can't even tell if it was unintentional since Sasuke didn't comment on his use of it.
As for Kakashi, he's seen Itachi's mangekyou with his own, and has only witnessed tsukiyomi. He somehow accessed his own sharingan's mangekyou and developed a jutsu for it which has no relation to amaterasu or tsukiyomi.
You've already bolded the issue, we can't tell.
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Haku... could do super ice jutsu, with no training at all. Heck he probably didn't even want to hurt his parents, but in his emotional state he created those ice spikes that destroyed his house and killed them.
Is that anime?
And you are somewhat wrong. Haku "trained", much like a baby "trains" to walk. His bloodline was discovered because he had been using it.
Anyhow, it is clear that those with bloodline have an extra ability with which to fight. For instance, the byakugan is directly a very nice tool. But kaiten and the open palm style based on it don't rely on the doujutsu.
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His tool is vastly more awesome than what most ninja have however, and underneath that, he doesn't have that many abilities that make him far better than most ninja.
This is where you're clearly wrong. You can be immensely gifted and not do much with your gift. Itachi became strong because he worked hard and hard work would have made him very strong even without his gift. Unlike his peers from his clan, Itachi grew far bigger than what just the sharingan could give him. Seriously, we saw him take down three Uchihas with their sharingan out and we know how much single Uchihas are feared already.
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The 4th, seems to have had enough of a hand in managing how the 9-tails would be sealed to be able to appear as a spirit in Naruto's consciousness when needed. This is actually more akin to Orochimaru's accomplishment in creating that inner world for soul transfer, than Itachi's accomplishment of using the mangekyou to create a genjutsu like tsukoyomi.
wat
srsly wat
saske raped orochimaru's world with basic sharingan and his genjutsu knowledge
saske appeared in naruto's consciousness and raped kyuubi with basic sharingan and genjutsu knowledge again
(saske also broke tsukiyomi but we don't even know how much itachi resisted against that, but then saske did experience tsukiyomi a lot)
srsly you don't even know anything about how any of this work (nor do i)
wat are you comparing