I can share that here in Denmark we have a system exactly like that, and have for more than a decade. It's called "NemID" (lit: EasyID), soon to be changed to "MitId" (lit: MyID). While there definitely are some problems with the current implementation, having a 2-factor auth solution in front of every government, banking, insurance, etc. web service is very helpful. [0]
Keep in mind that my only interaction with individuals from the government, on the phone or otherwise, is when picking up books at the library and renewing my passport. Everything from filing my taxes through registering a child for school to reporting a move is done with a NemID login and a simple, guided form. [1]
My taxes are pre-filled with the information they've already gathered from my employer and the bank through which I handle my stock portfolio. The only thing I manually have to put in is my union fees and how many times I drove to the office -- both giving me a sizable deduction.
Doing my taxes at the end of the year is simply a formality too. At the start of the year I do an advance statement with what I expect to earn, and my monthly taxes are automatically pulled based on that. The end-of-year tax calculation is to ensure I didn't pay too much or too little -- the difference being due either way in April.
All of this to say -- a sane, digitized interaction with public institutions is not only a possibility but a fact in certain countries.
[0]: https://en.wikipedia.org/wiki/NemID -- the entry is critical but not unfair. The MitID changes mitigate many of the big points.
[1]: https://lifeindenmark.borger.dk/ -- It's both a "guide to Denmark" but also has the aforementioned forms. Try going through the "Health insurance card" order flow. You can't accidentally order one without a login.