What is the purpose of this "transference" of holiness and how was it effective?
45. Take the Levites instead of all the firstborns among the children of Israel and the Levites' animals instead of their animals, and the Levites shall be Mine I am the Lord. מה. קַח אֶת הַלְוִיִּם תַּחַת כָּל בְּכוֹר בִּבְנֵי יִשְׂרָאֵל וְאֶת בֶּהֱמַת הַלְוִיִּם תַּחַת בְּהֶמְתָּם וְהָיוּ לִי הַלְוִיִּם אֲנִי יְהוָֹה:
In order to give a possible answer we have to understand what this "transference" of holiness accomplished. The, apparent, reason for this holiness is the ability to perform the sacrificial service. This is seen from the Gemara in Zevachim (112b) where it describes the job of the firstborns before the transference of holiness.
BEFORE THE TABERNACLE WAS SET UP BAMOTH WERE PERMITTED AND THE SERVICE WAS PERFORMED BY THE FIRSTBORN; AFTER THE TABERNACLE WAS SET UP BAMOTH WERE FORBIDDEN AND THE SERVICE WAS PERFORMED BY PRIESTS.
הנה הבכורים נתקדשו להיות לשם מעת שציוה (שמות יג ב): קדש לי כל בכור בבני ישראל באדם וגו'. והיו בכורים רבים בישראל, ולא נפדו עד הנה, שעדין לא נאמר למי יהיה הפדיון, כי עתה הוא שנתקדשו הכוהנים ועדין לא נצטוו במתנות הכהונה. והנה הם עומדים בקדושתן סתם, ויתכן שהייתה בהן עבודת הקורבנות כדברי רבותינו (זבחים קיב ב).ב).
Behold, the firstborns were made holy to G-D from the point when it was commanded (Shemos 13:2) "Make holy for me all of the male [human] firstborns of Israel etc." There were many firstborns in Israel and they were not redeemed (replaced) until now because it still was not said who it would be redeeming them. Even now that the Kohanim (priests) were sanctified there was still no commandment about the gifts that are given to the Kohanim. Behold, they (the firstborns) were standing with their simple holiness. It is possible that they (the firstborns) were performing the sacrificial service, like our Rabbis said (Zevachim 112b).
ועתה החליפם בלווים והם פדיונם, וציוה שיפדו הנותרים, ונתן הפדיון לאהרן ולבניו כאשר היא מצווה לדורות.
Now (in this Parsha) [the firstborns] were swapped with the Levites and they were redeemed and it was commanded that the remainders (the extra 273 that had no Levite counterpart) be redeemed [through money.] The money redemption was given to Aharon and his sons just like the [redeeming of the first born] commandment that was for the generations (in the future).
קח את הלוים תחת כל בכור בבני ישראל: מה שאין הלוים של עכשיו פודין את הבכורות הנולדים לישראל מכאן ולהבא היינו טעמא שהרי הלוים של עכשיו נולדו מאבותיהם הלוים שכבר פדו בכורי ישראל ואין הדין נותן שיהיה להם כח לפדות אותו יותר מפעם אחת וכל הבכורות של עכשיו אינם מבכורות שנפדו כבר בלוים במדבר אלא נולדים הם מפשוטי ישראל שלא נפדו מעולם והבכורות שנפדו בלוים במדבר אינן ידועין לפטור את הבאים מהן
Take the Levites instead of all the firstborns among the children of Israel: [The reason] the current Levites (In the time of Chizkuni) can not redeem (replace) the firstborns that are born to [regular] Israelites now and in the future is because the current Levites were born from their fathers, the Levites that already redeemed (replaced) the firstborns of Israel and the law does not give them the power to redeem more than one time. Also, all of the firstborns now are not from the firstborns that were already redeemed (replaced) by the Levites in the desert, rather they are from regular Israelites that were never redeemed (replaced) and the firstborns that were redeemed (replaced) with the Levites in the desert did not know to permit (basically, redeem or replace the future firstborns with Levites) the [children] that came from them (the people that were not redeemed).
מצות עשה לפדות כל איש מישראל בנו שהוא בכור לאמו הישראלית שנאמר כל פטר רחם לי. ונאמר אך פדה תפדה את בכור האדם:
תחת כל בכור פטר רחם בבני ישראל בתחלה היתה העבודה בבכורות ולפי שקלקלו בעגל, זכו לוים על שלא טעו בעגל ליכנס תחתיהם. כי לי כל בכור וגו' כמה דתימא: קדש לי כל בכור וגו', לי יהיו אני ה'. לפי שהוא אומר: ואני הנה לקחתי את הלוים מתוך בני ישראל תחת כל בכור שומע אני מיום ההוא ואילך לא יהיו הבכורות קדושים?! ת"ל: יהיו מלמד שהם צריכין פדיון
"[The Levites were chosen] in the place of every firstborn, opening of the womb, of Israel (Bamidbar 3:12)." In the beginning, the sacrificial service was done by the firstborns and because they became spoiled through the [sin of the Golden] Calf the Levites merited to take their place because they did not err with the [Golden] Calf. "Because every firstborn is mine etc (ibid 3:13)." It is like that which is said: "Make holy for me every firstborn...for me they will be, I am G-D(ibid)." Because He said: I, behold, I am taking the Levites from the midst of Israel in the place of every firstborn. Should I think that from that day and onward the firstborns are no longer holy? [The Torah] comes to teach us with the words "they will be" that they (the firstborns) need to be redeemed (because they are still holy).
The final idea I want to delve into that will complete this discussion is why did the sin of the "Golden Calf" cause the firstborns to lose their right to serve in the sacrificial service? Why was it that the sin of the "Golden Calf," a sin that only a small minority of Jewish people participated in, was so detrimental to the firstborns that they needed to hand over their holiness to the Levites? For this, we have to understand the nature of the holiness of the firstborn. For this idea I will use a Sefer called Eretz Chemda (Bamidbar 3:12):
Just like the firstborn is the first for impurity so too he is the first for holiness. Meaning, if impurity occurs, it is an extreme occurrence of impurity (they are the leaders). [On the other hand,] if holiness occurs, it is an extreme occurrence of holiness (They are the leaders). This that is written (Shemos 13:3), "Moses said to the people, 'Remember this day, when you went out of Egypt,'" was stated because the firstborns of Egypt sinned because of the impurity that occurred in them. So too, the firstborns of Israel are sanctified because of the holiness that occurs in them (This is why the previous verse of Shemos 13:2 talks about the holiness of the first born of Israel)...Behold, before the sin of the "Golden Calf" the sacrificial service was done [by the firstborns] without [their] choice and their holiness came from above (the firstborns were imbued with holiness from G-D) and because of this the firstborns are holy. However, after the sin of the "Golden Calf" the holiness (for performing the sacrificial service) came from below (the people had to imbue themselves with holiness)...And this that it says (Bamidbar 3:12), "As for Me I have taken the Levites from among the children of Israel in place of all firstborns among the children of Israel, who have opened the womb," The reason for "the Levites shall be Mine" is because they chose to be (the Levites imbued themselves with holiness). [However, when the verse says (Bamidbar 3:13)] "For all the firstborns are Mine," that is because of the inherent holiness [they were created with.] For when all of the firstborns of Egypt were struck down, right then [G-D] sanctified the [Jewish] firstborns. However, once the sin [of the "Golden Calf" occurred] the sacrificial service was taken from the firstborns and given to the Levites.
26. So Moses stood in the gate of the camp and said: "Whoever is for the Lord, [let him come] to me!" And all the sons of Levi gathered around him. כו. וַיַּעֲמֹד משֶׁה בְּשַׁעַר הַמַּחֲנֶה וַיֹּאמֶר מִי לַיהֹוָה אֵלָי וַיֵּאָסְפוּ אֵלָיו כָּל בְּנֵי לֵוִי: