Okay, so the first thing I must admit is that I am a mathematical dunce so there are factors that may be beyond my comprehension. That may even be one of the problems with this question in this regard: Some of the necessary evidence is outside of our specific field of expertise.
However, insofar as what I can consider, I suspect that the problem is with additional unknown or otherwise incalculable factors which further complicate the question beyond your expectations.
First of all, this might not be a question that can be answered purely by mathematics. The volition of the females to be in a relationship with a particular somebody, let alone a polyamorous one, may be an incalculable factor. Asuna's willingness to be with Kirito is probably predicated on a presumption of chastity, or in other words his ability to be faithful to a monogamous relationship. Kirito's charisma is considered to be especially high, and in an abstracted question like this it is difficult to ignore that he is the protagonist of the story, which may increase his odds of success beyond that of the average extra.
Second of all, how do you determine the average cross/gender encounter rate? If we assume that a woman has the same odds of being added to a harem at any given time, then odds of creating a heterosexual harem are zero percent if the player base is completely segregated for the entire duration of the game, and perhaps each time a person meets increases the likelihood that this person can be added to the harem. Now we know for a fact that it is not, but I suspect we still need to know how often people of opposite genders interacted within two years.
How many people constitute a harem? Can it be as few as three or five, or do there have to be at least a dozen women for it to count? You say at least five here, but it is not expressly stated in the question so it is left ambiguous for anybody viewing the question on the main site, and we base a question's open/closed status based upon the content of the question there.
Also, you should take note that your exemplary harem is impossible:
Please remember that Sachi can not be in Kirito's harem because she dies before any of the other prospective members are introduced. We need to consider how the death rate affects the odds of being able to build a harem over the course of two years.
Now some of these concerns can be hypothetically addressed if we know enough of the facts of the story, and a question that can be based in facts is usually not Primarily Opinion Based. Moreover, S.A.O. is the sort of story that divulges demographical information, so it is probably one of the better candidates for this type of question because they are more likely to exist in this tale and we are better suited to knowing those facts than a mathematician. In this regard, I am not sure if the question is exactly P.O.B., but I think these are the sorts of factors which may have been considered, and they certainly seems to be a very complicated one that would be difficult to answer.
More importantly, I have difficulty believing that the volition factor can be anything other than pure guesswork, which is probably adequate grounds enough for closure unless a study can be produced which demonstrates otherwise.
One incidental note I would like to add is that, working with assumed rates may solve the P.O.B. issue by giving us objective numbers to work with, but at the same time it would distance it from being an actual question regarding the show so much as the numbers derived from it, and risk putting it outside of our scope.
