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 All the "hardware wallet" implementations for Bitcoin show that you can make a secure element for BIP340 just fine. 
 Specialized SEs != TPMs in computers, SEs in phones, etc 
 Ah yes correct. 
 BIP340 are Schnorr signatures?

From: https://trustedcomputinggroup.org/wp-content/uploads/TPM-Rev-2.0-Part-1-Architecture-01.07-2014-03-13.pdf

Section: C.4.3 EC Schnorr

"If a TPM supports ECC, it should support the TPM_ALG_ECSCHNORR scheme."