Even if serial means "one night at a time", so long as each man is only going home with one woman per night, there will still be an equal number of unattached women and men.

If all people were forced to be copulating at all times then your conclusion regarding equal access would follow. An acceptable weirdtopia!

All people being obliged to copulate at, and only at, specific times would also lead to the conclusion. A less acceptable weirdtopia.

As it happens it is possible for some males with exceptional attractiveness, skills and motivation to mate with a different female every day while some females do not mate every day. This allows for the possibility that there is not equal access to mates among all members of the population in question.