As far as I understand the word, utilitarianism means summing people's welfare; if you place any intrinsic value on equality, you aren't any kind of utilitarian.

Utilitarianism means computing a utility function. It doesn't AFAIK have to be a sum.

If in all the axioms of the expected utility theorem you replace lotteries by distributions of individual welfare, then the theorem proves that you have to accept utilitarianism. People who place intrinsic value on inequality would deny that some of the axioms, like maybe transitivity or independence, hold for distributions of individual welfare. And the question now is, if they're not necessarily irrational to do so, is it necessarily irrational to deny the same axioms as applying to merely possible worlds?

(average utilitarianism, that is)

YES YES YES! Thank you!

You're the first person to understand.

The theorem doesn't actually prove it, because you need to account for different people having different weights in the combination function; and more especially for comparing situations with different population sizes.

And who knows, total utilities across two different populations might turn out to be incommensurate.