From the Department of State web site, a passport can take "up to 18 weeks from the day an application is submitted to the day a new passport is received." For expedited service, this can take "up to 12 weeks" which is divided up into "6 weeks for processing and up to 6 weeks for mailing times on the front and back end." Furthermore, it says you can "Pay an extra $17.56 for 1-2 day delivery for the return of your completed passport."
It's unclear how much time this 1-2 day delivery could shave off the 12 week service. Since it says up to 6 weeks mailing time (which is the same as for non-expedited service) but mentions both front and back end components (which I assume could mean it takes some time to move through the internal mailing system before it actually gets sent out) I assume this means that it could shave anywhere from no time at all all the way up to 5 weeks and 5 days from the time. So there does not seem to be any guarantee that a passport can be obtained in under 12 weeks. And if one has a non-refundable airline ticket and their passport arrives even one day late all the money paid for the ticket and any part of the trip could be lost.
Suppose that one needs their (first) passport in 13 or 14 weeks. It would seem that the 12 week window is sufficient, until one goes to make an appointment and finds that no acceptance facility within 50 miles has any appointments until at least 4 weeks from now. Now suddenly it seems impossible to guarantee that one will receive their passport in time even with expedited shipping.
On the other hand, the only faster service seems to be limited to "life or death emergencies" defined by needing a passport "within 72 hours due to a qualifying life or death emergency" or urgent non-emergency travel which also seems to have a 3 business day window and requires proof of travel.
What does one do in such a situation where their travel time is non-emergency and non-urgent, and is sufficiently in advance to be beyond the expedited service time from the current date but is sooner than the expedited window due to the lack of appointments to start the process?
Update: I also looked at some "agencies" near me. They make claims which seem to contradict the "Department of State" suggesting things like you can get your passport in 10 weeks without them, and also have many horrible one-star reviews on how they are a scam, make promises they can't keep, prey on people in a rush, and can't do anything more than you can get directly from the government.