No matter how many of McGee's bets you take, you can always take one more bet and expect an even higher payoff. It's like asking for the largest integer. There isn't one, and there isn't an optimal plan in McGee's dilemma.

Yes, the inability to name a largest number seems to underlie the infinity utility paradoxes. Which is to say, they aren't really paradoxes of utility unless one believes that "name a number and I'll give you that many dollars" is also a paradox of utility. (Or "...and I'll give you that many units of utility")

It's true that the genie can always correct the wisher by pointing out that the wisher could have accepted one more offer, but in the straightforward "X dollars" example the genie can also always correct the wisher along the same lines by naming a larger number of dollars that he could have asked for.

It doesn't prove that the wisher doesn't want to maximize utility, it proves that the wisher cannot name a largest number, which isn't about his preferences.