Nevada's DMV is a great example what happens without eID. Agencies that have a better idea about people's identity have been forced to do things like background checks and fingerprinting. Your data eggs in one basket, or a few.
If you attack the DMV in a country that has working eID it will only affect the DMV. Maybe you can't sign up for a driving exam or order new plates. That's it. It won't affect the police in cases that don't concern the DMV (like insurance) and vice versa. Sure if you attack everything at once everything will be affected, that's always an option, eID or not.
Fundamentally a digital ID does not mean a single "basket", just that wherever those "eggs" are that you know it's one single "chicken". That "chicken" can also have multiple ways of identifying themselves (including offline methods). That's how it is in countries that have a working eID implemented.
And now we know what Estonia's single point of failure is.
An adversary only has to hack one system to bring an entire country down. That sounds a bit scary to me.