I think how well a pyramid design performs depends on how you define performance. If you only look at fps, then among straight-stave bows with no recurves or reflex, a pyramid is a superior design (in my opinion).
Performance, as in FPS? If so, at what arrow mass?
you could also look at bow efficiency, how much of the energy that entered the draw is actually (and potentially) translated to arrow speed.
See for example Kooi & Bergman 1997, who compared efficiency of different bow designs.
https://www.researchgate.net/publication/285362259_An_approach_to_the_study_of_ancient_archery_using_mathematical_modellingBut for flight shooting, efficiency doesn't matter, rather arrow speed with very light arrows (dry fire speed).
this is where static recurves can shine. At 10 gpp, however, they don't perform better than the best straight self bows. Since pyramids inherently optimize mass versus strain in the lower limbs, just like ELBs actually, they can have higher dry fire speed than other straight bow designs. But at high arrow masses, this difference hardly matters.
Look for example at the broadhead flight records: they hardly differ between selfbow, sinew-backed recurves (I assume these are the most likely simple composite) and complex composite recurves (sinew-wood-horn recurves).
http://www.usflightarchery.com/pdf/2017-Flight-Records-Broadhead.pdfThe difference is marked, however, when comparing regular flight archery
http://www.usflightarchery.com/pdf/2017-Flight-Records-Regular.pdf
