That's not a dominance hierarchy, though.

Male lions mostly don't form a dominance hierarchy. It's might-makes-right. Prides usually have one adult male, and he maintains his position by not being such an incredible jerk that all the females turn on him, and by being stronger and fiercer than any males who might try to contest his rule. One or two subordinate males are usually tolerated (often sons of the dominant male who weren't kicked out / haven't been kicked out yet), but there isn't much ranking going on among male lions as a whole.

Most species of baboon form a very unstable male hierarchy: although numerous other males in the tribe are permitted, status is usually quite tenuous, resulting in frequent fights to maintain positioning. (Females tend to have their own stable hierarchy.)

Chimpanzees form a much more stable dominance hierarchy, with relative position being maintained with politics more than fighting, and threat displays also more than fighting.

Most male lions die without reproducing. Most male chimpanzees do reproduce (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2689943/).

So, as I said, dominance hierarchies do reduce fighting among males. It's not perfect, but it's pretty effective.