No. USB-PD is not a "firehose". That is not how electricity works. USB-PD specifies certain discrete voltage levels, but you can draw as much or as little current as you want. Devices are supposed to have a buck converter to adapt the voltage of the input to the voltage of the battery, and they can do so at a wide range of input voltages.
The only reason to raise the voltage at the USB connector is to reduce resistive losses in the cable by reducing the required current. Once the electricity arrives at the device it can be converted to whatever voltage is appropriate for the battery, and it can deliver exactly as much current as it should. There is absolutely no reason whatsoever why USB-PD would cause more damage to a battery than Qualcomm QC, in a correctly designed device.