I've never experienced any government process where paying a third party would have simplified things. I've also never heard of any third party offerings for that purpose. Could you share some examples?

Not sure about now, but last year your only way of getting a digital vignette for the Austrian highway that is valid “today” was via a third party (from outside Austria, I think).

Austrian ASFINAG would only sell you one that is valid in ~2 week at the earliest, since that’s the time you are guaranteed by law to return it. Not very handy if you are already on the road, and don’t want to stop to buy a physical vignette.

It generally means someone translating your information to the format the government employees expect, because each attempt costs multiple weeks of waiting. Basically, if there is a 6-week response time, you want to get it right on the first try.

In other cases, you pay people to save yourself the hassle of fighting for an appointment slot, and to save a trip across town in the middle of a work day. These fixers become the somewhat digital layer to a famously analog bureaucracy.