Since like my second year programming I stopped writing branched code totally, few tens of thousands lines of code in, I haven't encounter anything that intrinsically requires speculative branch prediction, like logically.

But I write only numes.

Is there any program that can't be written without a branching that can't be rephrased (literally, all that is is rephrasing) into branchless?

Mind risc-v don't offer BPU, there's extensions but not in the requirements.