It depends how you define madness I guess. But we were actually talking about SAN primarily.
My contention is that a lower SAN is inevitable if you understand Mythos stuff. You might not go insane immediately I agree. But you will be closer to going insane, and more likely to go insane.
There's also a lot of stuff in Lovecraft where people don't full understand stuff until they're losing it.
I don't agree. They're intertwined. There's literally no human in Lovecraft who understands this stuff and is still fully sane. That's not arguable. If such a character existed, they'd stand out as a dumb Mary Sue-type character in defiance of the norms of the setting, but they don't, not in Lovecraft (possibly in a derivative writer but I can't think of one off-hand).
Now you're redefining SAN outside the DMG definition, though.
It's a possible to define a stat that isn't SAN that does what you want, you might actually call Alienation or something (ALN). The more Alienation you have, the easier it is to understand Mythos stuff and the less damaged you are by contact with Mythos stuff, but as your ALN goes up, you'd check to gain what seem to mere human minds, madnesses. When ALN exceeds 20 you go out of play.
This would align with the Mythos. As you become less human through knowing more truths, you would understand stuff even better, and the madness checks should be when you gain ALN, not lose it - and yeah it makes sense that you'd do better with psychic attacks and stuff.
However, that's not SAN as per the DMG.
The problem with SAN is that it goes down and that makes you less able to "understand the ranting of a madman", for example. That doesn't track with the Mythos. SAN goes down when you fail SAN saves and suffer madnesses. Yet when that happens to Mythos characters, they become more likely to understand the rantings of a madman - there's a lot of "FINALLY I COULD SEE!" stuff.
Underneath the hood, I think the problem is that they tried to have a single mechanic serve two masters with different needs. SAN is meant to be a sort of "death spiral" mechanic, making it more and more likely that you fail certain saves and go crazy and fail saves and go crazy and so on. But they also try and use it as an "Occult" stat, to understand weird happenings, which doesn't make sense at all.
So here's an approach that could work:
You have TWO new stats. SAN and ALN. Ok. So SAN you create normally (roll, buy, etc.). ALN is 20 minus SAN. So if you have a SAN of 14, you have an ALN of 6. Maybe the player just picks the stats and they have to total to 20.
SAN is used only for saves. It's used for pretty much the same things as suggested.
ALN is only used for ability checks, and is used solely for understanding things humans should not be able to understand. Like you should not be able to understand what some ranting madman is actually talking about, but if your ALN is high enough, maybe you do. And so on. Pretty much the same list as before.
If you fail a SAN save, and your SAN is 11 or above, roll a d20, on a 10 or more nothing happens, less than 10, lose 1 SAN and gain 1 ALN.
If you fail a SAN save, and your SAN is between 10 and 4, roll a d20, on a 10 or more, you can choose to lose 1 SAN and gain 1 ALN or gain one short-duration madness. Less than 10, lose 1 SAN and gain 1 ALN or gain a long-term madness.
If you sail a SAN save and your SAN is 3 or less, lose 1 SAN and gain one indefinite madness.
(We'd need a better and more thematic set of "madnesses" here, preferably one that isn't really real-world insanity-based, but more "how people go mad in Lovecraft"-based to minimize or even eliminate disability-shaming etc. - more dramatic and ridiculous and not real stuff like depression or outright delusion - indeed any delusions should be Mythos truths, if somewhat misunderstood)
Whenever you roll 20 on a ALN ability check you can choose to gain 1 ALN and lose 1 SAN.
Anyway, this is like a quarter-arsed system and I'd need someone to write the Mythos-appropriate "madnesses" but I think it would do the job better than what is suggested in the DMG.
