I've looked around best I could, but couldn't find a good answer to this. Is there any place it's documented publicly as to why the soft fork was called Taproot?

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This was answered in the Bitcoin Optech "Preparing for Taproot" series (2021):

“I always assumed the origin of the name was ‘taps into the Merkle root’, but I don’t actually know what Gregory Maxwell’s thinking was.” —Pieter Wuille (source)

“I originally had to look the word up; but I took it as the key path being the ‘taproot’ because that’s the tasty one that you make carrot soup out of, and the merklized scripts would be the other lesser roots that you hope to ignore.” —Anthony Towns (source)

“The name originated in a visualization of a tree with a thick central truck like a dandelion taproot—the technique is mostly useful because of the assumption that there is one high probability path and the rest is fuzzy stragglers, and I thought it was a good one because of the punny fact that it verifies script-path spends by tapping into the hidden commitment in the root.

[…] Alas, calling the hash tree with the sorted interior nodes a ‘myrtle tree’ didn’t catch on. (Myrtle tree because the set of policies with an equal hash root are ones whos ordering differs by a permutation which can be defined by a t-function, and Myrtle is the family which includes melaleuca, the tea-tree, and it sounds like ‘merkle’. :p )” —Gregory Maxwell (source)

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