can I just say that calling it "reverse-harem" feels really silly? (I know you didn't coin the term, this isn't a callout to you).
But why is it when it's a girl character collecting dudes it's "reverse harem" and not just "harem". Because "reverse" makes me think it'd be a bunch of people collecting one person as their shared ....uh, person.
The word "harem" has actual origin, rather precise meaning and long history (arabic, women's wing of the house/female members of the family, and probably over a thousand years). In western world (and/or english language) it exists for few hundreds of years, and usually means a group of women (wives/concubines/slaves) of a single man, especially if we are not talking specifically about arab world.
We are not talking about arab world here, so we can safely ignore original meaning and just focus on western one, even if it's hundreds of years younger.
Then, we also need to take into account marriage standards across the world, even taking into account different cultures and times. We have monogamy, which wasn't always as prevalent as it's now (especially outside of broadly defined western world), and we have polygamy.
Lets focus on polygamy, you have 2 basic types - polygyny and polyandry.
Lets also take into account that theoretically man can have thousands of children (because he can impregnate multiple women at once), woman can have what, 20 at most (because she can be in only one pregnancy at a time). We are talking at least 2 orders of magnitude theoretically, 1 order of magnitude in practice (and rather common historically).
Polygyny - one man with multiple wives, which historically allow a successful man to have more offspring, bring no doubt who is the father of the kid (there's only one man and mother is always known for obvious reasons), and also gives the control over the group to the physically stronger man (so basically if women don't play together nice man can force them to if he wants - and has the ability to do so).
This is also model that probably naturally evolved in societies that were more aggressive (more war = more conquest = disproportion between men and women, because men die at war and women don't, also there are female captives from conquered regions, as often men were killed and women were taken captive, to be mothers of the next generation of warriors).
This was probably the most common model for thousands of years (occasional or regular polygyny).
Then, we have polyandry - one woman, multiple men. This model has no advantages from polygyny, and everything that was a benefit there is a problem here. The number of societies it was practiced in you could count on your fingers (Tibet being probably most known example here). And husbands usually were brothers or other close family members.
It had only one benefit - in situations where work of a single man was not enough to sustain a family, it allowed them to have a family at all. It was not a result of some matriarchal society, it was a result of extreme poverty, that you had no real ways to get out of.
So yes, regardless of more recent societal norms (give or take last hundred years), using harem for polygyny and reverse harem for polyandry has actually pretty good reasoning behind it.
Adding "Reverse" when it's an FMC just feels weirdly skeevy to me, I dunno. Like it's somehow so "out of the ordinary" that a whole new term was needed instead of just using the same one because it's the same concept.
It actually WAS so out of the ordinary. It was never the same concept, and even now it is not, even if we take into account the more recent changes in societal norms, that i don't really want to get into.
Thought experiment - imagine a uninhabited island, with enough resources to sustain a group of people in the hundreds indefinitely.
You drop 10 men and 100 women there - after few years (or few dozen years) you'll probably have somehow functioning, small society, which started with these 10 men and their harems.
You drop 100 men and 10 women - in months, and i'm being generous here you'll have a mountain of corpses, from men fighting over women, with a high chance of no women surviving it at all.