I'm not sure which point you're referring to with the mention of differing API. Mobile BankID is the same API as regular BankID (but services can choose which they accept); as for other Swedish e-ID services, there are aggregator services.
Re: most, really? There are some that don't accept non-mobile BankID, but it is uncommon in my experience.
> There is also already a clear precedent to allow delegation of access that require strong authentication IRL.
Sure, but what does that have to do with BankID itself? Both in-person and online, it is the service that decides whether someone else can act for you. And various services do offer this: I can let others access my tax records or prescription medicine records online.
I don't think it's unreasonable for services to want to know who they're dealing with. In real life, if someone else shows my ID at postnord, they have to show their own ID too.