There's a EU directive instructing on how citizens should be able to identify online with eIDAS. In my country, you can use eIDAS to authenticate in basically any governmental agency portal, but you can't get any eIDAS enabled auth method as a citizen. The current way of authenticating is done via bank accounts or a paid extra mobile service that requires a non-prepaid mobile contract.
This is a relatively huge issue. First off, the Finnish government pays the banks for each auth any user does when they for example want to log into their medical records etc. It's a few million euros a year just for verifying the users.
There's also obviously issues with whom the banks serve, there has been some cases with them not taking foreigners or people with bad credit as customers, making it impossible for them to authenticate themselves.
The current EU directives also indirectly require that the banks should provide a bank customer the possibility to authenticate without needing to have a banking account (which costs money), but to my knowledge this still isn't possible. I pay around 20 euros a month just for the luxury of having an account, not everyone can afford that on top of other bills.
Auth services are not accessible for impaired users.
It's also basically impossible to manage who has essentially the power of attorney and over which matters, for how long etc. Either you have to give them your login info (good luck resetting your SSN) or try to use the services over the phone and somehow convince the other side that you have permission to manage things for another person.
There's no ways of authenticating who is using your accounts online and actually verify the users.
Basically, my idea is combining biometrics, PGP and having the government running the identity management themselves. This would have added benefits of basically enabling hashed throwaway addresses and info for use online while providing a free and accessible way of authenticating strongly online.