The laws of eglah arufah are very similar to those of the scapegoat from the Yom Kippur service. In both cases an unworked animal is taken to an uninhabited location, and is killed by an atypical method, after which our hands and/or body must be washed. And in both cases priests are present as we request atonement ("kaparah") for sins which may have been committed.
It therefore seems that the purpose of the two procedures is identical: to symbolize that we are receiving atonement, that the sin(s) are literally being removed from our midst.
The only difference is that while the scapegoat is integrated into the formal Temple service, the eglah arufah takes place locally (depending on where the corpse is discovered) and thus is independent of the Temple service.
The laws both immediately before and after eglah arufah concern various aspects of war. We would therefore expect that eglah arufah is also related to war, and the discovery of unattended corpses in the field is certainly compatible with that. Perhaps each city has a responsibility to absorb and protect any civilians who happen to be in the path of the armies. If the city shut its gates and left these people to their own devices, its leaders would in fact be culpable if the civilians ended up getting killed.
"Thus says your Lord - Hashem; and your God - who advocates/struggles ["yariv"] for his people..." (Yeshayahu 51:22 - this week's haftarah)
Biblical poetry is notable for its frequent use of parallelism, where one phrase is followed by a second phrase with the same meaning but different choice of words. This is clearly the case here, where "your Lord" in the first phrase parallels "your God" in the second.
But what about the second half of each phrase? If this verse is following the common pattern, then the proper name "Hashem" must parallel the description "advocates for his people". This would be unusual, in that a proper name is juxtaposed with a description.
But perhaps this is a fortuitous source which allows us to define the meaning of the name "Hashem". Based on the parallelism, it seems the name "Hashem" by definition implies particularistic intervention on behalf of the Jewish people. This is in opposition to names such as "Elokim" and "Shadai", which refer to the same God, but which relate to more universal/natural behavior by God.
We could perhaps have reached the same conclusion, by looking at the patterns of name usage in Tanach. But that would be difficult, since other factors often complicate the choice of names, and the patterns are not 100% consistent. In contrast, in this verse, the definition is virtually explicit.