Our attempt at the walk-in post office was an epic fail. We arrived an hour early and the queue was already approximately 60 people deep. It's hard to tell how many actual passport applicants were among the 60 people (there were a few kids with parents), but if we assume 50 and ten minutes per applicant, we're talking about a 4+ hour wait for the two people processing applications.

This assumes it really would be two people working the entire time, and the both would be willing to work 2 hours past the posted time for passports, as it's only a 2 hour window to begin with. Since we're talking about a government worker culture here, I wasn't willing to bet on that. We left.

To AMflier's point, some cities have other entities that handle passports. As it turns out, Orange County, California has several of its county offices do it. They have an online appointment booking process and availability 3 weeks out. So we're set up to go there in mid-March, first appointment slot of the day, so hopefully it will be rather painless.

If you're in Kansas City and need a passport that requires an in-person application, the only advice I have is to start the process months in advance. Walk in to a post office and make an appointment for 4-6 weeks later.