Good question. We could call "fun" the achievement of what you address above: the illusion of success, since everyone plays games for it.
Well, in part. There are aesthetics of play that aren't heavily involved in "success" like community and sensation, but yes, I think when you were thinking about what "fun" was you were very much thinking about the illusion of success because it's that aesthetic most threatened when you aren't doing something or when what you do is nullified by failure.
But if a min-maxer stays with the game when succeed/fail is no longer an issue (#3), is it because he intends to continue to min-max, or because the need to min-max is no longer there, providing other ways to find illusory success?
First, there is no such thing as a game where succeed/fail is no longer an issue. It's always there. Think of it this way - success for a min-max oriented player is defined as "getting my own way". The risk of not getting your own way is pretty much always there in any system that has fortune mechanics, even if it is one of those that has success on failure to one degree or the other. The only thing that differs is degrees of risk and what it means to have system mastery - that is, what skills it takes in particular to maximize your chances of "success".
Or put it this way, any game that has mechanics such that you can effect chance of getting what you want through chooses in character creation and play has a min-max outlet.
And that's pretty much every RPG ever.
In fact, games that have "success on failure" may be even more attractive to many min-max oriented players because it maximizes their chance of getting what they want. They aren't thinking "Well, even if I fail, I'll still have fun." They are thinking, "I can maximize the chance of getting what I want, and even if I don't get what I want immediately, I basically will get a reroll, thereby maximizing the chance of getting what I want." In this case, min-maxing is oriented both toward "winning big", where winning big means "more spectacularly than the other players" and "getting what I want as soon as possible." The aesthetic of the player hasn't changed just because you've provided different mechanics. He will absolutely continue to min-max because doing so maximizes his enjoyment.
There is a wonderful nigh definitive example of this in the 'Geek & Sundry' episode where they play the game FATE Core, nominally by mechanics and intention a narrativist oriented game with fail forward mechanics and low appeal (at least in theory) to gamist players whose motivation is "win now". As Wil Wheaton introduces the system, he calls it the "gold standard in getting the system out of the way so that the story can be the thing." Ironically, in 30 years of playing RPGs I've never seen a game session so dominated by system as the one that is presented. There are three players at the table. One of them, Wil Wheaton, obviously in CharGen intends to create a combat focused character who will take spotlight during combat encounters. However, Wil's system mastery turns out to be relatively low, leading to taking relatively little spotlight in the resulting play especially in combat situations (to some degree of evident frustration). On the other hand, John Rogers during CharGen and play demonstrates a massive amount of system mastery, allowing him to turn his character into a massively competent agent of basically anything he wants to be competent at, ultimately dominating play, accumulating spotlight, winning bigger than any other player in terms of illusion of success and validation from the GM that he's a winner, and demonstrating a great deal of skill in min/maxing in a system that is supposedly not about "winning".
There is absolutely nothing you can do mechanically to change someone's aesthetic tastes.