Not only from a player's perspective. According to my own reasoning, it seems the most mutually beneficial thing to do, from the average magus character's perspective, including members of mystery cults.
Think about it: the whole Order is built on a model of exchange of magical knowledge, for a fair price. Initation Scripts are not really different from Summae or Lab Texts. Very few mages would share them for free without just compensation, OTOH very few mages do not share their new insights and discoveries for a good price, and the history of the Order shows that almost all new discoveries, no matter how precious, if they can be reliably duplicated, unavoidably spread to the rest of the Order.
I see no concrete reason why Mystery Cults should work under a different model, since mystae are still Hermetic mages. It is more beneficial for a MC to work openly, and not to charge members too burdensome membership fees, since that means more influence, more members, more opportunity to develop their insights, and be free from the burden of maintaining excessive secrecy. It is better to reap a few services from a fifty members, than a lot from a dozen. They just have to ensure nobody gets training without due compensation. Sure, some MC may still maintain greater secrecy for ideological reasons, and charge 10 years of service for initiation, but social pressure would end up making them the minority.
Therefore, I do expect most Mystery Cults to eventually end up working like unofficial Houses, where they self-perpetuate themselves by charging new mages for training, but their existence and abilities is an open secret. IE I do not expect Esoteric cutls to work much differently from Exoteric ones, in the Order. The main difference is that they don't have official recognition, although nothing really stops from creating a setting where MC are an officially recognized social network which work parallely to the Houses. It would go for added options for political intrigue, and it would take but a Great Tribunal ruling.
I'm not saying it has to be the mandatory model, only that barring overwhelming reasons to the contrary, I deem it the most likely model to develop.
Other SG may want to postulate contrary powerful factors that manage to stymie the evolution of MC toward openness, and good for them. personally I quite loathe all this cloak and dagger conspiratorial stuff, and I see no overwhelming reason in the setting or rule system why it should be implemented nonetheless, instead of a model where Mc set up shop openly.
Cults are not necessarily focused on the mysteries of one svhool only, to the exclusion of any other insight. Many cults mix insights, e.g. alchemical and astrological insights.
But since IotS is so useful to immortal magi, and the cult is about pursuing it, it is more likely that some Mystagogue thought of developing a Script for it, and therefore it is more likely for the cult to have it, than the contrary. Both may happen. But given exceeding plot-driven reason to the contrary, it is more likely to the former than the latter.
The Order is, among other things, one big marketplace for the sharing of magical insights. This makes very very likely that MC which openly advertize and proselytize in the end will bloom and grow and become the dominant model, while the conspiratorial ones will become marginalized and likely only survive for the ones that strongly share their ideology. Successful MC will never die out, since new generations of mages will always be there in the need of Initiations for the Virtues they offer, but even if in your saga hasn't happened yet, it is unavoidable that MC will arise which are like the Children of Hermes in structure, and over time, they will become the dominant model. For the very same reasons why the OoH has become dominant among the magicians of Mythic Europe. Theirs is the most efficient, successful model for mages to propser, and the setting or the rule system provide no overwhelming reasons why the same model should not come to dominate MC, too. It may not have happened yet in your saga, just the way the OoH could not have arisen. But once it does, and takes some root, it will come to dominate the market, so to speak.
It may not happned yet in your saga, I concede it, but I contend that is the by far most likely course. So bear with me if I speak of it as the foreordained conclusion. 
This I readily concede. History is never entirely predictable. I just contend that barring exceptional and unforeseeable factors, my model is the most logical and mutually-beneficial and therefore likely to happen from hermetic magi POV.
Sure. This does not stop one vision to be more reasonable and likely to happen, the history and structure of the Order being the same.
On the latter point, let's agree to disagree. Given the ample place the social practices of the Order allow for secrecy, and the fact immortal magi have much less need for mundane support (they don't eat...) and therefore can afford seclusion much better, Mythic Europe could well harbor dozens or even a hundred of immortal magi between alchemical, faerie, animal, and ghost ones, not to mention Daimonic ones (even if they are likely to be the minority). Immortals are not in direct competititon for any resource but vis, and they have greately reduced need for it (no healing, no longevity), so they have limited reason for suppressing the birth of new immortals.
But being too tight-fisted about sharing their own powers is just what ensures your insights will eventually be stolen, repoduced, or reverse-engineered, as dissatisfied mages will work to experiment, self-initiate, steal Scripts, and set up shop as rival Cults. If there is something that history shows, is that keeping too tight a lid of the spread of information NEVER works, no matter how much force you apply. Knowledge can be, with extreme difficulty, destoryed, but not kept secret forever. The Essential Nature of Knowledge is to be Free. Mythic Europe is not that much different, as any new Hermetic discovery unavoidably spread out in the Order in a generation or two.
I assume that at the very most, a MC can hope to charge 2-3 years of service for every initiation they bestow, before members and perspective members grow dissatisfied and take steps to ensure that Initiation is available by other means. The very existence of Common Mystery Virtues, and the dissemination of the Automata mystery, is evidence that I'm right and that powerful social forces work in the Order to frustrate the efforts of greedy or paranoid mystagogues to keep their insights under too tight a lid.
The Children of Hermes are the wave of the future, just as Bonisagus was, like it or not. 
