What is the point of the Eglah Arufa?

Towards the very end of Shofetim, we are instructed in the laws of Eglah Arufah, which begins:

א כִּי-יִמָּצֵא חָלָל, בָּאֲדָמָה אֲשֶׁר ה' אֱלֹהֶיךָ נֹתֵן לְךָ לְרִשְׁתָּהּ, נֹפֵל, בַּשָּׂדֶה: לֹא נוֹדַע, מִי הִכָּהוּ.

1 If one be found slain in the land which the LORD thy God giveth thee to possess it, lying in the field, and it be not known who hath smitten him;

The entire ceremony seems somewhat weird and ritualistic, but not if you understand in its full poetic import.

Regardless, this is perhaps a motivation for Rambam to offer a highly rationalistic explanation of the whole ceremony. He explains, in Moreh Nevuchim, volume 3, chapter 40, that the arranging of the entire ceremony and involving of the elders of that city will cause there to be investigation as well as publicity. And this will get people talking, and thinking about the murder; and perhaps someone, even possibly not kasher le'edut, to come forth to identify the killer, or their strong suspicions of the killer. And that person could then be killed by Bet Din, or by the king outside the typical rules of jurisprudence; or else by the goel hadam. And since the land can never be used, this might impel the owner of the land {inherited as mentioned in pasuk 1 above, I would add} to try to save his land by investigating the murder.

The same idea is then put forth in the sefer Hachinuch, Mitzvah 530. He essentially channels the Rambam, that since everyone is going to want to see the spectacle, they will turn out in great numbers. And those who hear will quake and their thoughts will be awakened on the matter, such that anyone who knows will tell what he knows before the elders. In this way, they will eliminate the evildoers and murderers from among themselves. And another idea, also from the Rambam, that this will publicize among the people that the elders and men of knowledge wish to find the murderer to visit vengeance upon him on behalf of the victim.

Abarbanel, on his commentary on the parsha, also cited this Rambam in Moreh Nevuchim. He says basically the same thing, but ends by citing the RambaN's objection that while there is indeed this toelet, the details of the ritual do not bear out the stated shoresh. They should pick specifically the best field in the vicinity if the goal is to encourage the owner of the field to investigate the murder. And according to him {=RambaN's} position, there is some aspect of korban to this. And therefore Chazal list this among the Chukim.

Abarbanel's reaction to this is to explain each of the details of this ritual and its meaning. See inside.

Mincha Belula also gives this idea that it is to catch the murderer, but then concludes with a statement that the ways of Hashem are deeper than our comprehension; and also that Chazal say that it is a chok.

So is apparently the position of the מעמר, Rav Meir Wolf, in a commentary I have not seen inside.

Shadal, after briefly noting all this, argues. He writes:

א ] כי ימצא חלל : מצוות עגלה ערופה איננה למען יתגלה הרוצח ( כדעת הרמב " ם מורה חלק ג ' פרק מ '. ואחריו בעל ס ' החינוך ודון יצחק ובעל מנחה בלולה והמעמר ) , אלא לשתי כוונות : האחד , לחזק האמונה המפורסמת באומה שכל ישראל ערבם זה לזה ושלארץ לא יכופר לדם אשר שופך בה כי אם בדם שופכו ; ולכן אחרי שאין הרוצח ידוע להם ואל יוכלו לעשות בו דין , יערפו תחתיו העגלה וירחצו הזקנים את ידיהם , לסימן , כי הם ושולחיהם נקיים וכפיהם לא נגואלו בדם ההרוג .

והשנית , כדי שבתוקף אמונתם בעונש המגיע לארץ בשביל הדם אשר שופך בה, לא יבואו להרוג נקי שיהיה נחשד על הרציחה ההיא , בזולת ראיה גמורה ועדות ברורה . כי אמנם אעפ"י שיודעים היו שאין כל העם ערבים על מכה רעהו בסתר , היה אפשר להם לחשוב שזה אמנם אינו אלא כשאין ההרוג ידוע , אבל בנדון שלנו שהחלל נמצא , ייתכן שיהיו כל הקהל נענשים , אם לא ישתדלו עד שיימצא הרוצח

He asserts that the purpose is not to reveal the identity of the murderer, but rather for two reasons. Firstly, to strengthen the widespread belief of the people that all of Israel are guarantors for one another, and that the land will not accept atonement for the blood which was spilled upon it unless blood is spilled. And therefore, since the murderer is not known to them and they cannot render judgement upon him, the break the neck of the heifer in his place, and the elders wash their hands, as a sign that they and their agents are innocent, and their palms are not stained by the blood of the murdered person.

And the second reason, since in the might force of their faith in the punishment which will affect the earth because of the blood {of the victim} which was spilled on it, they not come to kill an innocent who happens to be suspected of this murder, unless there is complete evidence and clear testimony. For if not for this, even though they know that it is not so that all the nation are guarantors on one who smites his fellow in secret, it is possible for them to think that this, however, is only when the murder is not known, but in our case, where the corpse was found, it is possible that all the congregation would be punished, if they do not endeavor until they find the murderer.

Thus, Shadal views this as intended to push the nation towards one belief and to protect them from acting rashly on the basis of that same belief.