Sure, that's the theory, but I'm not sure a "SE-based" system as you describe it is actually used at all, or certainly for any non-trivial volume of transactions, in an Intel-based (desktop/laptop) environment.

I've never used a web store checkout system that wasn't based on browser forms, or any mechanism that felt like asking a secure enclave to sign a transaction. Google Chrome offers to store your credit card numbers for you, but that's just so it can autofill web forms.

Apple Pay or whatever, sure, on their hardware. Macbooks, I'd think it uses the touchbar secure enclave. But nothing really uses SGX on Intel except Netflix DRM.