The4 jury is still very much out on whether it happens. There has been a bit more research done since Cecil’s column was written, there have been controlled experiments done to counter most of Cecil’s criticisms and synchronisation now seems to be popularly accepted yet again. Not only that but it now appears that women will also synchronise if exposed to male pheromones.
As for why it occurs. Who knows there are endless hypotheses out there.
But I will point out the obvious flaws in the OP’s reasoning.
First off humans don’t have alpha males. We are social animals but not all social animals are like wolves. There is not and never has been pone male that breeds with all females in a group. In some small hunter-gatherer clans there may be only one mature make, his wife and children but that doesn’t make the one mature male the alpha male, it makes him the sole male. In larger groups humans behave just like they do in the US, forming stable partnerships with one male and one or more females dedicated to him.
So the idea that it’s problematic for the alpha male is just nonsense simply because the alpha male doesn’t exist and never did.
The second problem is that in numerous species where there are dominant males the females all come into oestrus simultaneously. This is true of rabbits and sheep for example. The idea of this may well be to spread the paternity of the group.
With sheep each male attempts to guard a harem, however there is a size limit to harems and as a result lesser males will invariably have the chance to mate so long as the population remains high. In other words in good conditions where there are high population numbers the animals get to take a risk and experiment with alternative genetics, while in stressful conditions the animals are restricted to the dominant males. It’s the best of both worlds.
Rabbits are much faster breeders than sheep and the males become devoted to one female for some time. This means that other females can readily be serviced by other bucks. Once again this produces a situation where the group gets a good spread of paternity and isn’t restricted solely to large heavy aggressive though slow males who can dominate rivals. Smaller faster and more timid males also produce offspring, and the benefits of both phenotypes to a species like the rabbits should be obvious.
The final problem of course is that the OP seems to assume that humans only mate when females are fertile. That is not the case. Indeed females themselves don’t know when they are fertile, much less the males. As a result it doesn’t matter one bit when they become fertile because the male may or may not be copulating with them at that time. It’s strictly a lottery.
One hypothesis for why humans do synchronise is that it means that all the wives of any man can not become pregnant simultaneously. Assuming the husband shares his attention amongst his wives over a period of days rather than changing partners daily the synchronisation should ensure that there is at least a month between births. That allows the earlier birthers to recover somewhat by the time the husband needs ot devote most attention to the next wife.
I’ve also heard exactly the opposite idea, that the synchronised cycles lead to synchronised births. Since milk constitution varies with the age of the infant this allowed women to nurse each other’s children thus enhancing the survival of the group.
In reality it probably makes no difference at all. For 99% of our history most women were perpetually pregnant or breastfeeding. No matter how synchronous cycles may become there’s no way of picking when a woman will cycle following birth. It might happen almost immediately, it may not happen until she finishes breastfeeding almost 2 years later and it can happen any time in between. Synchronisation just wouldn’t be very important realistically.