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To be fair Itachi hand no clue what CT was nor did he know how it worked. Also if Totsuka does come in contact with the core it definitely reaches it.
He learned how it worked the moment he saw it start to gather rock. It's not that hard a jutsu to decipher and none of what you just typed out changes a thing I said. The core reaches far too high for him to be able to cut it with Totsuka. That's why he used Yasaka Magatama in canon. If Totsuka was capable of reaching he wouldn't have told them to use long range attacks.