Pneumonia is a common fatal complication of influenza, and I think there's reasonably good statistical evidence that the cases counted towards flu deaths are mostly caused by the flu especially in the bad flu epidemic years which are most comparable to Covid-19. That sentence is a bit like claiming that people don't die from falling out of airplanes because the actual cause of death was hitting the ground.

I think you meant 'flu deaths are mostly caused by [bacterial] pneumonia'. One thought along those lines is that the spike in deaths we see is due to covid19 killing directly, death coming like clockwork X weeks after infection. Compared to the flu, which due to the requirement for a secondary bacterial pneumonia, has a higher variability in the timing of the death: at what time bacterial infection develops, which strain of bacteria, antibiotic interference, etc. Thus, we're going to see higher spikes for covid, and hopefully narrower.

Yeah, and apparently one of the more interesting consequences of this is that people don't necessarily have detectable flu virus anymore once they're hospitalized with pneumonia because it's the bacteria allowed in by the now-gone flu infection that's killing them.