It has to be a platinum coin because subsection (k) of https://www.law.cornell.edu/uscode/text/31/5112 is the special case that allows for issuing any denomination.

Notes are a liability of the Federal Reserve. Meaning they can be traded for balance on a Federal Reserve account. The treasury can't just create liabilities for the Fed out of thin air, I mean that would be wrong ;-)

(edit: just joking. The $1T coin would also be deposited at the Federal Reserve. I don't know why it can't be a note, other than that's how the law was written.)