Shoftim: Why the hands of the witnesses first?

An interesting idea I saw in Rabbenu Ephraim, on the pasuk in Shofetim (Devarim 17:7):

ז  יַד הָעֵדִים תִּהְיֶה-בּוֹ בָרִאשֹׁנָה, לַהֲמִיתוֹ, וְיַד כָּל-הָעָם, בָּאַחֲרֹנָה; וּבִעַרְתָּ הָרָע, מִקִּרְבֶּךָ.  {פ}

7 The hand of the witnesses shall be first upon him to put him to death, and afterward the hand of all the people. So thou shalt put away the evil from the midst of thee.

Rabbenu Ephraim writes:

יד העדים תהיה בו בראשונה להמיתו;
 מאי טעמא? שאם העידו עדות שקר יחול עליהם
 עונש שפיכת רמים — דם נקי, ויד כל העם
 באחרונה: דגברא קטילא קטלו
"The hand of the witnesses shall be first upon him to put him to death. What is the reason? That if they testified falsely, the punishment will fall upon them for the shedding of blood -- innocent blood.
and afterward the hand of all the people -- for [then] they are killing an already killed person."

I would say that this still is society carrying out, and enabling, his execution. So if they executed a person incorrectly, the fault still lies with society.

But it is an interesting idea, in which false witnesses are the ones who carry it out, and cannot imagine that they are simply standing back, or merely indirectly causing his death. And that can also stand as a deterrent against false witnesses.

Perhaps we can read it as part of the separation of evil from one's midst. Where does one's fealty lie? Elsewhere, in Reeh (Devarim 13), we see the tempter towards idolatry, the following idea -- note in particular the idea that יָדְךָ תִּהְיֶה-בּוֹ בָרִאשׁוֹנָה לַהֲמִיתוֹ; וְיַד כָּל-הָעָם, בָּאַחֲרֹנָה:

ז  כִּי יְסִיתְךָ אָחִיךָ בֶן-אִמֶּךָ אוֹ-בִנְךָ אוֹ-בִתְּךָ אוֹ אֵשֶׁת חֵיקֶךָ, אוֹ רֵעֲךָ אֲשֶׁר כְּנַפְשְׁךָ--בַּסֵּתֶר לֵאמֹר:  נֵלְכָה, וְנַעַבְדָה אֱלֹהִים אֲחֵרִים, אֲשֶׁר לֹא יָדַעְתָּ, אַתָּה וַאֲבֹתֶיךָ.	7 If thy brother, the son of thy mother, or thy son, or thy daughter, or the wife of thy bosom, or thy friend, that is as thine own soul, entice thee secretly, saying: 'Let us go and serve other gods,' which thou hast not known, thou, nor thy fathers;
ח  מֵאֱלֹהֵי הָעַמִּים, אֲשֶׁר סְבִיבֹתֵיכֶם, הַקְּרֹבִים אֵלֶיךָ, אוֹ הָרְחֹקִים מִמֶּךָּ--מִקְצֵה הָאָרֶץ, וְעַד-קְצֵה הָאָרֶץ.	8 of the gods of the peoples that are round about you, nigh unto thee, or far off from thee, from the one end of the earth even unto the other end of the earth;
ט  לֹא-תֹאבֶה לוֹ, וְלֹא תִשְׁמַע אֵלָיו; וְלֹא-תָחוֹס עֵינְךָ עָלָיו, וְלֹא-תַחְמֹל וְלֹא-תְכַסֶּה עָלָיו.	9 thou shalt not consent unto him, nor hearken unto him; neither shall thine eye pity him, neither shalt thou spare, neither shalt thou conceal him;
י  כִּי הָרֹג תַּהַרְגֶנּוּ, יָדְךָ תִּהְיֶה-בּוֹ בָרִאשׁוֹנָה לַהֲמִיתוֹ; וְיַד כָּל-הָעָם, בָּאַחֲרֹנָה.	10 but thou shalt surely kill him; thy hand shall be first upon him to put him to death, and afterwards the hand of all the people.

So maybe this is supposed to be the individual, and societal, reaction to idolatry. The idea is to engage in וּבִעַרְתָּ הָרָע מִקִּרְבֶּךָ, and thus reject this negative influence. And so those who witnessed it directly take action to uproot it, and the rest of society follows their lead.