I got feedback from some users that, depending on the load conditions powering up the Raspberry PI by connecting the USB connector sometimes is not working properly. I made several tests with different power supplys and finally I was able to reproduce the behavior.

The osciloscope view explains it best. Yellow is the voltage seen on the USB-C connector coming from the wall plug (scaling 1V/div). Blue is the voltage at the Raspberry PI pin 2 (+5V input) note the scaling is 1V/div. 

What is happening here. The powersupply was connected and serves 5.1V. After approx 2ms the LTC4041 enables its DCDC to supply the Raspberry PI. In addition to that it also starts to charge the Supercapacitor with approc 1A of current. The output voltage to the PI is raising but the wall plug gets overloaded which results in a voltage drop below(!) the shutdown voltage limit of the PI. At this limit the LTC stops charging, the load current drawn from the wall plug is now reduced by 1A and it recovers. Then the voltage raises above the power fail limit and the story repeats and repeats and ...

Only the usage of a good powersupply with enough internal blocking capacitors can avoid this kind of problems.