(Most) Bureaucrats don’t get a pension after 20 years, so that’s a bit of a red herring.

https://en.m.wikipedia.org/wiki/Federal_Employees_Retirement...

A relative of mine works for a state level LEO targeting financial crimes - they've spoken often about how "smaller government" advocating politicians have repeatedly hamstrung the organization when it tries to go after large corporations. They've still managed to do good work going after smaller scale offenders that fleece investors - but I wouldn't put the blame on those employees for doing work you don't find useful... it's mostly up to politics.

Any govt office, focusing on the US here, seems to have a huge back log and understaffed like the IRS, Immigration services, DMV etc. For e.g. earliest appointment I can get is perhaps a month or two out. A huge backlog and understaffed makes a case of overworked employees. Surely, they are doing work, and so I can only think that by "they do too little useful work", you mean that the work itself that they do is of little use. Are they? Seems like getting my driver's license or tax refund is pretty useful, no?

I've worked public and private sector and know plenty of people in both and I've not noticed a huge difference in the number of people just coasting vs those who really try to make a difference.

What makes you think government is that much worse than the private sector in this regard?