Based on the article I linked in my other comment I would say that on oxygen-rich planets, respiration is likely to happen simply because life needs to find a way to deal with it's toxicity, or perish. Although that presupposes that photosynthesis is inevitable, which also doesn't have to be true.
I kind of wonder how much we truly know about the strength of lock-in effects of evolution - of how much life is "stuck" with old hacks that we can no longer get rid of or that lead to dead ends. I doubt we'd ever evolve avian lungs from where we are now, for example. I know there are examples like that all over the place, but just how strong is the effect?
there are options. For example radiosynthesis like is done by these fungi discovered in Chernobyl https://en.wikipedia.org/wiki/Radiotrophic_fungus