In order to see such a story, someone would have had to do contact-tracing of a large number of people with covid back to a single flight they all were on. Given the haphazard nature of contact tracing (in the U.S. at least) it is quite plausible that large-scale transmission events on airplanes are happening but simply aren't being noticed because we're not looking for them.
That said, the ventilation in planes is pretty good, and if everyone is wearing a mask it's equally plausible that air travel is relatively safe.
As with anything else, including sitting in a restaurant or bar, any single flight is unlikely to infect you and statistically "safe" from the perspective of individual risk. But air travel is absolutely spreading this disease.
The whole notion of treating a pandemic via the lens of individual risk ("will I get sick if I do this one thing") is broken analysis, of course. But at this point I despair of our ever being able to free ourselves of that nonsense. It's just too ingrained.
How would you determine this without solid contact-tracing? Nearly all of the cases where I'm at are associated with "international travel", so at least some of that has to come from planes.
More changes costs some incremental fuel (as it siphons pressurized bleed air), but the effect is quite small.