If the number of reactor designs is equal to the number of reactors built IRL, then of course the historical data would fail to distinguish those factors.
I went and did looked up some stats from aviation, since that's an industry that would be able to distinguish them and operates in a comparable safety-and-reliability regime. Here's a graph of count of active Boeing 474s by year: https://www.iba.aero/insight/evolution-of-the-boeing-747-fle.... Pay attention to the bright blue showing the count of active hulls. Now compare that to the rate of 474 hull losses: https://en.wikipedia.org/wiki/Boeing_747_hull_losses. Note that the rate of hull losses is basically flat - there were just about as many 474s lost in the 1970s, with only 200 hulls active, as there were in the 2000s with 1200 hulls active, and as there were in the 2010s with 600 hulls active. At worst logarithmic, and I wouldn't be surprised if that's the actual way that failures are probabilistically exposed by increased hull count. I also didn't do any work to exclude "ate a SAM" and other causes that are independent of the airframe. Either way, in a healthy, scaled-out fleet, failure rate is a function of the design much more than it is a function of the fleet size.
We are not talking about aircraft, we are talking about nuclear plants. The one is a lightweight aluminum structure for carrying passengers and cargo, the other is a massive structure to generate energy. Not sure how you could confuse the two.
With respect to serialization, failure rates, reliability, safety culture, and response to failures, then yes, I assert that a widely-deployed nuclear reactor design would behave much more like an airplane design than it would a design from any other industry. Two-digit or three-digit unit counts, very tight regulatory requirements, immediate and visible human safety implications for major failures, most of the line's production is active concurrently, extremely attentive and active maintenance with good communication and agile response to failures, very little divergence from the plan to account for local details. For comparison, I didn't use any of these:
* Cars, because those have millions of units with distributed inattentive owners that can't do stop-the-world refits
* Rockets, because they're disposable and built-and-used serially rather than in parallel
* Hydroelectric dams and skyscrapers and bridges, because those must be 100% bespoke (due to terrain or artistic flourishes) and have no replaceable parts
* Datacenters, because those are either non-safety-critical (AWS et al) or bespoke (ADP et al)
* Hospitals and corporations and governments, because those are 100% bespoke (due to organizational "terrain" i.e. individual leaders)
* Satellites, because those have *no* maintenance
* Oil refineries, because those are 100% bespoke
* Roads, because those have no replaceable parts and no catastrophic cascading failures
Large, high-production-count ships might have worked, things like container ships and warships, but those have very few catastrophic cascading engineering failures - ships that are big enough to be useful (that is, that work like reactors rather than cars) are lost in wars or because they get driven into rocks, not because a single turbine blade failed while the ship was doing a triple reverse backflip over the international date line.
Semisubmersible mobile offshore drilling rigs (i.e. oil platforms) might have been another good comparison. I'll have to go look up stats on those; they look to be in serialized production and with double-digit unit counts per design, and vulnerable to the same kinds of subtle and complex cascading failures that nuclear reactors are vulnerable to (e.g. https://en.wikipedia.org/wiki/Ocean_Ranger#Causes_and_effect...). That said, I don't know how many of them sink, and it looks like they don't operate under anything even vaguely similar to the same safety and reliability regimes that reactors do, nor does the oil industry improve at all in response to failures.
For the purposes of safety and reliability as a function of serialization, nuclear reactors and airplanes are more alike than they are different.
(and, like, really, materials are your argument? They both use turbines, they both use hydraulics, they both care critically about fluid flow, they both require active stabilization and fail deadly if uncontrolled, they both require continuous maintenance from dozens of trained specialists, they both have corrosion and fatigue as primary concerns, etc etc etc.)
I went and did looked up some stats from aviation, since that's an industry that would be able to distinguish them and operates in a comparable safety-and-reliability regime. Here's a graph of count of active Boeing 474s by year: https://www.iba.aero/insight/evolution-of-the-boeing-747-fle.... Pay attention to the bright blue showing the count of active hulls. Now compare that to the rate of 474 hull losses: https://en.wikipedia.org/wiki/Boeing_747_hull_losses. Note that the rate of hull losses is basically flat - there were just about as many 474s lost in the 1970s, with only 200 hulls active, as there were in the 2000s with 1200 hulls active, and as there were in the 2010s with 600 hulls active. At worst logarithmic, and I wouldn't be surprised if that's the actual way that failures are probabilistically exposed by increased hull count. I also didn't do any work to exclude "ate a SAM" and other causes that are independent of the airframe. Either way, in a healthy, scaled-out fleet, failure rate is a function of the design much more than it is a function of the fleet size.