If your utility were defined over all possible futures, you wouldn't speak of maximizing expected utility. You would speak of maximizing utility.

The utility function defined on lotteries is the expectation value of the utility function defined on futures, so maximizing one means maximizing the expectation value of the other. When we say "maximizing expected utility" we're referring to the utility function defined on futures, not the utility function defined on lotteries. (As far as I know, all such utility functions are by definition defined over all possible futures; else the formalism wouldn't work.)

edit: you seem to be thinking in terms of maximizing the expectation of some number stored in your brain, but you should be thinking more in terms of maximizing the expectation of some number Platonically attached to each possible future.