“the purpose of the Techeiles strings is so you see them and get reminded of all the things that Techeiles is supposed to remind you of. If so then he did not need to make a Tallis shekula Techeiles in order to make this argument.”
Korach has a 1 – 2 punch. First he had the populist view that we are all holy and don’t need the techeilet reminder string (Moshe). Next he asked if a house is full of sefarim does it need a mezuzah? The halachah is that it does not (although we customarily do put on mezuzot in our shuls which have sifrei Torah). Korach pointed to the contradiction between the needed reminder of tzitzit (regardless of the techeilet beged) and the “unneeded” reminder of mezuzah in a shul.
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“For example he could have just held Techeiles in his hand and asserted that his regular Tallis should be patur from Techeiles. “
And if you were to tell me that there might be some quantataive difference between techeilet and mezuzah, a talit comprised of 100% techailet would be refute that. But in both cases they have to be attached of the item.
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“it was a collosal waste of time and resources.”
Not for someone filthy rich and power hungry.