Immortals' Learning – is there a point without them having a

[Wanderer]

@The Fixer

Wanderer, you seem to play in a game in which almost any virtue can be easily initiated in any cult, and in which these same virtues seem to be somewhat common knowledge.

Not so radical, except for cults that are purposefully syncretistic like the Children of Hermes. Rather, I do assume that any cult has Scripts for any Virtue that would highly useful for their awowed goals (since past Mystagogues would have been spurred to develop them), and that the existence of all the main Mystery Virtues is known within the Order to any mage that has a decent OoH Lore (peculiarities of the Gift and special insights do get noticed by sodales), and that any mage with a decent Mystery Cult Lore knows all the Virtues (and Ordeals) that such a cult commonly initiates.

I do expect mystae magi to be secretive where it matters: i.e. not to share Scripts or to perform an Initiation without due compensation. It is true that as rule I would not expect hermetic magi to indulge in secrecy for secrecy's sake, mystae included. It does not vibe well at all with the mentality of a magical researcher. I do expect mystery cults to work more like elitist colleges with expensive tuition fees than conspiracies. Mystery Cults (except the Infernal ones) do stand to gain very little from trying too hard to suppress widespread rumors about their very existence or the abilities they can bestow. Therefore I do not expect Mystery Cults to be any more than an open secret.

Fine if this suits you and your game, but this is not the only vision of the game, and, in games where this isn't the norm, IotS may very well be almost unknown outside of a few circles of initiates. So, even if you can self-initiate it, you could very well have magi that don't, just because they don't know this is possible at all, for exemple.
=> Immortal magi without IotS

The "few circles of initiates" you mention ought to include the members of a mystery cult that has immortality as a goal. The main cases when I would expect an immortal magus not to have IotS would be a) when a Cult purposefully shun it for ideological reasons or because the other methods of the Cult make it unpractical (e.g. a Verditius cult) b) a mage wholly self-initiated his path to immortality and was not even cognizant that it existed c) he gained immortality as the effect of an unpredictable and unplanned sudden saga event, such as eating the fruits of the Garden of Hesperides.