The post office seems to be able to compete with Fedex and UPS. I've sent packages using all three, and the post office is as good as any.
Last time I took a package to the Post Office, the clerk fed the zip code into a computer, and told me that the zip and the city on the address didn't match. It turned out I had mistaken the zip, so my package would no doubt have been delayed had the post office personnel not been alert and on top of things. Not only that, but I've never gone into our local PO and seen " one Joe blow working, while three others sit in the corner chatting about nothing, while a line of people stretches out the door."
Maybe your local post office is different.
Now, let's talk about the evil DMV, prime example of state government incompetence.
I had been renewing my driver's license by mail until my face and the photo no longer matched very well. The DMV sent me a renewal notice, and I had to come in.
I made an appointment, unlike most of the patrons sitting around waiting.
I checked my watch while entering the building. Two minutes before the appointed time.
I went in, got a picture taken, a vision test, a thumb print, paid my money, and left. The time: appointment plus three minutes.
Government doesn't have to be slow, bureaucratic and wasteful. Some departments do work.