No principled reason, but unless he and the woman are wearing hats or something marking them as not-doing-the-procreation-signaling-thing, the cultural standard could still reasonably be that he does. Or not. It's not a big deal. My point is only that it's a reasonable signal to display and to want displayed for a lot of people. And at a baseline it certainly isn't a dominance signal, though humans are pretty good at turning any random thing into a dominance signal.

There's a ton of flexibility for how to implement this as reasonable cultural norms. It's not a big deal for some people to adopt a norm whose purpose doesn't apply to them as long as the effort required is small. It's also not a big deal if the norm is you don't have to adopt the behavior if it doesn't apply to you. It's also not a big deal if we skip some norms as long as the tradeoff isn't too bad. It is a big deal if people viciously attack each others' character for following a different norm than their own preference, especially if they infer malevolence for the other norm without clear and compelling evidence that this is in fact the source.