In one of the most common processor architectures (the x86 family), comparison operations do store their result into a register, but it's the flags register, which can't be used directly in arithmetic operations. So you have to follow a comparison operation with either a conditional branch or a conditional move (and earlier processors in the x86 family didn't have conditional moves).

> So I guess my question is, while it’s technically possible for a compiler to compile this into a branching operations, under what circumstances would a compiler actually choose to do that, given there’s isn’t a clear benefit?

It depends on the compiler heuristics and on the surrounding code; for instance, it might decide that "compare; conditional branch over next instruction; increment" is better than "copy to second register; increment second register; compare; conditional move from second register", because it uses one less register (the x86 family is register starved) and one less instruction (relevant when optimizing for size).