On the other hand, the USPTO patent database is nearly impossible for anyone other than a professional to navigate. Their search sucks.
Since you mentioned taxes: the fact that Intuit and H&R Block have successfully prevented the IRS from doing what nearly everyone wants: file your taxes for you, for free. For the vast majority of taxpayers, they could do that, yet the political pressure from paid tax preparers have prevented it, at least up to now.
And this illustrates the flaw with your starry-eyed Pollyanna-ism: no matter how honest & hard-working the bureaucrats might be, they're still accountable to corrupt pressures.
The 1950 census data, recently released, also sucks. To find one family whose exact address I wasn't sure of, I had to manually open about 50 strips of census taker daily records and decipher the hand-written names & addresses. Merely finding these 50 strips took more effort than nearly anyone would exert.
Their Search failed to find the family. I don't anyone could figure this out unless they were extremely motivated.
And last but certainly not least, let's look at the Obamacare website rollout, which got a Cabinet secretary fired.
So don't give us a couple good anecdotes and say, "look, the government works great!"
At my job I use APIs from the EPA and EIA, and they are stable, well-documented, and generally pleasant to use. I can also email an actual human with questions and get quick responses, which I can't do with Google.
I think whoever manages these services would do an excellent job running a mapping service or Places API, although obviously it would be hard to get traction now that Google Maps is so established.
Some of the features that make Google Maps useful, like GPS and public transit arrival times, are already based on government services.