Good question and the answer is not well known by the public and it seems somewhat counter intuitive. I had the same concerns but as it turns out the opposite is true. Most other primers, while generally having thinner or softer cups, the #34 has one of the lowest failure to fire rates of all large rifle primers because of the consistency of external and internal tolerances. The most significant factor affecting FTF rates among various types and brands of primers is not the thickness or hardness of the cup but the overall consistency of the dimensional tolerances. Anecdotally, I’ve never had a FTF with the CCI #34.
Early on in my conversion to the 34, I asked a friend who regularly rubs elbows with various R&D people in the firearms/ammo industry about exactly these types of questions. He provided me the info I posted above. So no worries, IMO, really about the #34 itself. There are many other things that have much more affect on primer reliability, proper ignition and powder burn. Like: contamination, pocket dimensions, primer seating pressure, anvil compression, powder compression and type of powder… , etc.