From a technical aspect I agree that it's definitely solved! I'm building my service on top of PKI for this reason.
The problem lies with the issuing and trust. Many countries do not issue e-IDs and it's not easy for a business to support all the ones that do. Take for example my country, Sweden. Basically every single citizen has an e-ID and it's used for everything. Yet I can't use it if I want to sign up for a non-Swedish service such as Revolut, N26, Transferwise etc.
The problem lies with the issuing and trust. Many countries do not issue e-IDs and it's not easy for a business to support all the ones that do. Take for example my country, Sweden. Basically every single citizen has an e-ID and it's used for everything. Yet I can't use it if I want to sign up for a non-Swedish service such as Revolut, N26, Transferwise etc.