Since the private pilot Part 61 minimums are only 40 hours compared to 250 hours for the commercial with a wide range of other minimum training and experience requirements, your argument is without merit.
Looking at hours doesn't really say much. A private pilot can have 1000's of hours without ever having gone for a higher certificate/commercial while a commercial pilot can have 250 hours.
This is again an issue of how we measure experience. Is a 250 hour commercial pilot who has 44 hours of 50NM XC time, 4hours of100NM XC time and 2 hours on a single 300NM XC time and 200 hours of flying in and out of the same airport (i.e. no other XC time as defined under 61.1) inherently safer than the private pilot flying the bush or making regular flights from coast to coast with different origins, destinations and intermediate fuel stops?
I would posit the answer to that question is no; a pilot with a commercial pilot certificate is not inherently any safer than a private pilot by virtue of their certificate or even their hours.
Most accidents (49.1%) were conducted with individuals holding a private pilot certificate. Second in incidence were commercial pilots (28.2%), followed by Airline Transport Pilots (ATPs) (13.7%), and student pilots (5.7%) (AOPA, 2012). Private pilots represent 30.8% of certificates held but have a much higher rate of accidents (FAA, 2012).
I'm reading the Nall 2015 report right now. The 2015 non-commercial fixed-wing accident rates shows GA Accident rates of 481 accidents or 49.2% by PPL holders, 261 accidents or 26.7% by CPL holders and 125 or 12.8% by ATPs.
The issue/question I still have about the Nall report though echoes
@Kritchlow 's earlier statement though... It does not show the total number of GA operations performed by the various certificate holders nor is it a "total accident count."
It could be completely possible (though improbable in the extreme) that every ATP that goes up GA results in an accident while only every other PPL that goes up GA results in an accident. Who/which is safer? The 100% accident rate of an ATP or the 50% accident rate of a PPL? Just because PPL's account for a higher total number of accidents does not necessarily mean they are not as safe as a CPL or ATP, it could (and likely) just mean they perform more GA operations than the typical CPL or ATP.
This is aptly illustrated by the Commercial Fixed-Wing Accident rates which shows Part 135 Cargo and Charter Accidents occur at a rate of 13 or 50% by CPL holders and 13 or 50% by ATP holders. Are commercial pilots really as skilled/safe as an ATP or conversely an ATP just as risky as a commercial pilot?
For Part 137 Aerial Application Accidents occur at a rate of 45 or 88.2% by CPL holders and 6 or 11.8% by ATP holders... Is a CPL holder really 8 times more likely than a ATP holder to have an Aerial Application Accident?
The correlation between these numbers are not so direct that such conclusions can be reached.
If we add non-commercial accidents and commercial accidents together we end up with the number of PPL accidents remaining the same and a decrease to 45.6% of total acccidents while CPL's number of accidents is up 22% to 319 with an increase to 30.2% of all accidents and the number of accidents involving an ATP increases 15% to 144 with an increase to 13.6% of all accidents. This also ignores flights accidents both commercial and non-commercial where a CFI is onboard (such flights seem to be attributed to the level of pilot receiving instruction and are not attributed at the level of the CFI who is at least a commercial pilot).
Additionally, in theory, commercial operators should have a lower rate of mechanical failures though in reality the rates show that the rate of accidents due to mechanical error actually increases though ultimately the accident rate attributed to pilot/mechanical/other errors do not differ significantly between commercial and non-commercial operations (73.8% non-commercial vs 70.1% commercial - Pilot error, 15.7% non-commercial vs 18.2% commercial - mechanical error and 10.4% non-commercial vs 11.7% commercial - other/unknown error)
Lastly, the correlation to the number of issued certificates also seems to be a bit off to me. First off the FAA statistics show approximately 41.8% PPL holders not 30.8% in 2012 (188,001 PPL, 116,400 CPL and 145,590 ATP). Using more recent stats according to the FAA statistics, in 2018 there were 163,695 PPL holders (38.4%), 99,880 CPL holders (23.5%) and 162,145 ATP holders (38.1%).
PPLs make up 38.4% of certificate holders in 2018; that does mean that at 49.2% of accidents they account for approximately 128% of their fair share of accidents but I dont believe it fair to look at a direct comparison that includes all ATPs as it has been my general observation that a significant majority of ATP's dont fly GA.
If we say only half of the ATP's fly GA aircraft (which still seems like a high number too me), the share of PPL's increases to 47.5% while CPL's make up 28.9% and ATP's make up 23.5%. At those numbers, PPL's account for 103.5% of their fair share of non-commercial GA accidents, CPL's account for 92.4% of their fair share and ATP's make up just 54.5% of their fair share of accidents.
If we factor in the commercial GA accident rates, the numbers change further with PPL's accounting for 96% of their fair share, CPL's accounting for 104.5% of their fair share and ATP's account for 57.9% of their fair share.
So yeah the numbers lack the context required to really determine what it is they are saying about the overall safety of a PPL vs CPL vs ATP. Considering PPL's are more likely to fly GA and specifically non-commercial GA than their CPL or ATP counterparts, I would expect they make up the majority of the accident rate flying under those conditions.