I think there's something here, but I still don't find the link from the far view to underdog support entirely convincing.

Why do we think why would we want to signal niceness in the far view? And why should signaling "niceness" involve supporting the underdog? (I mean this question in the evolutionary sense: why would our intutions of niceness correspond to supporting underdogs, and why would we value that signal?) And why would it allow us to portray ourselves as steadfast allies, if we don't actually have any connection to either of the parties involved?

Two alternative (not necessarily much more convincing) accounts, both based on the idea that in the far view, we don't need to think about the costs of our opinions so much, but which are otherwise somewhat incompatible with each other:

(1) If we know we won't actually have to do anything, supporting the weaker party is a cheap signal of strength. Only the strong would back a loser. (Maybe this supports your account, by giving a reason to signal "niceness"?)

(2) If we know we don't actually have to get involved, we just go with whoever we actually have the most sympathy for. (This is like your "niceness" explanation, but sans signaling.) Two versions:

(a) Most people just have more sympathy for weaker parties. Why? I don't know. (Not much of an explanation then is it?)

(b) People sympathize with the side most similar to them. (This would predict that the strong will generally have less of an underdog bias, and that if the underdog is sufficiently weak, then average types may switch to backing the favorite. This doesn't seem entirely implausible, but I have no idea whether it's contradicted by any evidence out there already.)