"Your SSH keys" aren't really part of that threat model. "You" know the device you're connecting from (or to, though generally it's the client that's the mobile/untrusted thing). It's... yours. Or under your control.
All the stuff in the article about how the TPM contents can't be extracted is true, but missing the point. Yes, you need your own (outer) credentials to extract access to the (inner) credentials, which is no more or less true than just using your own credentials in the first place via something boring like a passphrase. It's an extra layer of indirection without value if all the hardware is yours.
TPMs and secure enclaves only matter when there's a third party watching[1] who needs to know the transaction is legitimate.
[1] An employer, a bank, a cloud service provider, a mobile platform vendor, etc... This stuff has value! But not to you.