why bother with entropy as such?

Because it's one of the more obvious descriptive statistics to look at and it shows the difference nice and clearly. If we just say "the initial conditions need explaining" (or: the differences between initial and final) then the obvious question is what about the initial conditions, and part of the answer to that is going to be the entropy. (Or maybe some other thing that's essentially equivalent.)

Also, because it's a statistic that not only is different between the distant past and the distant future, but also varies in a consistent way at present.

I do not understand how these two paragraphs are a response to what I said. Can you elucidate?

I can try, but if they aren't then my best guess is that I didn't correctly understand what you were saying (which was less than 100% clear to me). So I'll be brief about the elucidation, and then whichever of us turns out to have been misunderstood first can do the next round of elucidating :-).

It looked to me as if you were saying, more or less, that entropy is a silly thing to be looking at at all, because it describes only our state of ignorance and not the actual universe; that when we say "the universe seems to be evolving from a low-entropy state to a high-entropy state" all we really mean is something like "we know a lot more about the past of the universe than about its future".

I, on the other hand, think that is a wrong (i.e., a less than maximally useful) way to look at it. Yes, a notion of entropy depends on some state of knowledge and observational ability. But that doesn't mean it depends on picking ours in particular, and there are not-so-arbitrary ways to do it.

Electroweak unification.

Noun phrase!

Would you like to make your argument a little more explicit? Do you think that weak parity violation is responsible for the familiar macro-scale time asymmetries everyone notices?

Well, then, that solves the problem

Only in so far as it's plausible that the asymmetry-in-the-laws that we found actually causes the asymmetry-in-our-observations that we're trying to explain. I don't see that it is plausible, but perhaps the words "electroweak unification" should have enlightened me?