I wrote an answer, but upon rereading, I'm not sure it's answering your particular doubts. It might though, so here:

Well, if we're talking about utilitarianism specifically, there are two sides to the answer. First, you favour the optimization-that-is-you more than others because you know for sure that it implements utilitarianism and others don't (thus having it around longer makes utilitarianism more likely to come to fruition). Basically the reason why Harry decides not to sacrifice himself in HPMoR. And second, you're right, there may well be a point where you should just sacrifice yourself for the greater good if you're a utilitarian, although that doesn't really have much to do with dissolution of personal identity.

But I think a better answer might be that:

If I have the choice, I might as well choose some other set of these moments, because as you said, "why not"?

You do not, in fact, have the choice. Or maybe you do, but it's not meaningfully different from deciding to care about some other person (or group of people) to the exclusion of yourself if you believe in personal identity, and there is no additional motivation for doing so. If you mean something similar to Eliezer writing "how do I know I won't be Britney +5 five seconds from now" in the original post, that question actually relies on a concept of personal identity and is undefined without it. There's not really a classical "you" that's "you" right now, and five seconds from now there will still be no "you" (although obviously there's still a bunch of molecules following some patterns, and we can assume they'll keep following similar patterns in five seconds, there's just no sense in which they could become Britney).