Cause of high failure rate in SC189 buck regulator
The main problem was that the input capacitor was ceramic with a low ESR. As it quickly charges up on startup, inductance in the wire and in the USB battery supply 5V source cause the capacitor to overshoot its voltage up to 6.7V+ which can apparently kill the SC189 with repeated exposure to this voltage, as it has an absolute maximum of 6V.

The solution was pointed out by @mkeith, and is addressed extensively in the application note Ceramic Input Capacitors Can Cause Overvoltage Transients

By putting a electrolytic 4.7 uF capacitor in parallel with C10, the two capacitors are not able to charge as fast and the electrolytic apparently starts to absorb the charge that the ceramic capacitor gets on startup, giving us a similar shape as before, but at safe lower voltages. I got the following figure, showing the over-voltage condition has been mitigated. Since there is still the weird non-monotonic start, I should probably use a larger capacitor.