No. This is a problem that was intentionally caused by Finansiell ID-teknik, and I'm not going to get into cat-and-mouse game to fix their for-profit product.
> Having read the BankId specs, they're "different" APIs in only in how the session is initiated. You're still challenged to enter the PIN for the certificate, which prompts the response to the authentication request. In other words, BankId and Mobile Bank Id are presenting the same exact set of data back to the session initiator.
They're different in that a service that takes Mobile BankID does not automatically support the desktop version, or vice versa. Whether the API is similar after that doesn't matter.
> I have, as of yet, to run into anything that would not take BankId or Mobile Bank Id.
Off the top of my head, Swish and Hemfrid only accept Mobile BankID, with no alternate authentication options. Swedbank accepts Mobile BankID or their custom OTP hardware token, but not desktop BankID.