Data points for processing time for 2 children's passports sent at the same time. Both were sent with expedited processing and expedited, 1-2 day delivery:

• Fri Dec 9: Dropped off at USPS acceptance facility.
• Tues Dec 13: I noticed that the checks had been electronically deposited.
• Sat Dec 24: (after checking daily) The U.S. Passport Application Status website finally updated to show "Application Status: In Process" with an application locator number.
• Tues Dec 27: received an automated email that "Application Status: Shipped" along with USPS tracking numbers.
• Wed Dec 28: received both passports via USPS 1-day delivery.

Total processing time from USPS drop off to receipt was just shy of 3 weeks, 19 days total. FWIW, the passports were actually issued on Dec 23, so the website only generated a locator number after it was already completed and waiting to be shipped.