Not saying that the PPQ is unsafe....but let me point out something, based on experience, which might put the issue into perspective.
I had a striker-fired pistol that operated similarly to the PPQ - that is, fully cocked when a round was in the chamber (and it couldn't be carried loaded without this condition). A very small part, a portion of the SA sear assembly, broke, causing the pistol to go full automatic. Granted, as I was firing the pistol at the time and I probably held the trigger back during the FA "event" (while hanging on to keep the muzzle under control).....it is possible that the event might have stopped with only "doubling"....if I had released the trigger. Nevertheless, understand that, if a similar internal failure occurred with the PPQ, the ONLY thing that would prevent an accidental discharge would be the FP block. Those devices, consisting only of a spring-loaded plunger, are NOT "fool-proof". They CAN stick, if dirt and residue are allowed to build up in them. They are hard to clean, because of the tight space in which they reside. AND with virtually all of the pistols so-equipped on the market, a sticking FP block is UNDETECTABLE to the shooter, until something goes wrong.
With the totality of that in mind, no one should EVER completely trust the FP block on ANY pistol. So, a fully cocked, loaded pistol is NEVER completely safe....and even less so, if the FP block is ultimately the "only line of defense" in case of the failure of another part.
This is why, at this point in history, I will NOT have a pistol that cannot be carried completely UN-COCKED, if a round is in the chamber. This includes, for me, the "partial-cocked" types, such as the Glocks. There is only a REMOTE chance that problems would ever occur....but I am not willing to take that chance myself. What everyone else does is their business.