How do we know that לולב צריך אגד?

There is a dispute between Rabbi Yehuda and the Chachamim whether לולב צריך אגד, if the lulav bundle needs to be tied. We pasken like the Chachamim that it does not, though in practice on the street, we see people using lulavim to bind their lulav bundles, which is a requirement only according to Rabbi Yehuda.

What is Rabbi Yehuda's source? The (setama de-)gemara discusses it on Succah 33a:

דתניא לולב בין אגוד בין שאינו אגוד כשר ר' יהודה אומר אגוד כשר שאינו אגוד פסול 

מאי טעמא דר' יהודה יליף לקיחה לקיחה מאגודת אזוב כתיב הכא (ויקרא כג, מ) ולקחתם לכם ביום הראשון וכתיב התם (שמות יב, כב) ולקחתם אגודת אזוב מה להלן אגודה אף כאן אגודה ורבנן לית להו לקיחה לקיחה 

מאן תנא להא דת"ר לולב מצוה לאוגדו ואם לא אגדו כשר מגי אי רבי יהודה כי לא אגדו אמאי כשר אי רבנן מאי מצוה קא עביד לעולם רבנן ומצוה משום (שמות טו, ב) זה אלי ואנוהו:

The brayta just gives the dispute, but the setama degemara gives the Scriptural basis. Namely, that Rabbi Yehuda learns a gezeira shava from the parallel use of the word ולקחתם.

it has been taught: A lulab, whether [the other prescribed species were] bound with it or not, is valid. R. Judah says, If it is bound [with the others] it is valid; if it is unbound, it is invalid.35 

What is the reason of R. Judah? — He deduces it from the word ‘take’ [which occurs here and with] the bundle of hyssop. It is written here, And ye shall take on the first day,36 and there it is written And ye shall take a bundle of hyssop.37 Just as there [it must be] a bundle, so here also [it must be] a bundle. And the Rabbis?38 - They make no deduction from the mention of the word ‘take’ in the two passages. 

Who is it that learned that which our Rabbis have taught: It is a pious deed to bind the lulab, but [even] if he did not bind it, it is valid? Now who is it? If R. Judah be suggested, why is it valid if he did not bind it? If the Rabbis are suggested, what pious deed does he perform?39 — It is in fact the Rabbis, and the pious deed spoken of is due to ‘This is my God and I will glorify Him’.40

The relevant pesukim are:

ויקרא 23:40:

וּלְקַחְתֶּם לָכֶם בַּיּוֹם הָרִאשׁוֹן פְּרִי עֵץ הָדָר כַּפֹּת תְּמָרִים וַעֲנַף עֵץ עָבֹת וְעַרְבֵי נָחַל וּשְׂמַחְתֶּם לִפְנֵי ה אֱלֹהֵיכֶם שִׁבְעַת יָמִים.

שמות 12:22:

וּלְקַחְתֶּם אֲגֻדַּת אֵזוֹב וּטְבַלְתֶּם בַּדָּם אֲשֶׁר בַּסַּף וְהִגַּעְתֶּם אֶל הַמַּשְׁקוֹף וְאֶל שְׁתֵּי הַמְּזוּזֹת מִן הַדָּם אֲשֶׁר בַּסָּף וְאַתֶּם לֹא תֵצְאוּ אִישׁ מִפֶּתַח בֵּיתוֹ עַד בֹּקֶר.

שמו 15:2:

עָזִּי וְזִמְרָת יָהּ וַיְהִי לִי לִישׁוּעָה זֶה אֵלִי וְאַנְוֵהוּ אֱלֹהֵי אָבִי וַאֲרֹמְמֶנְהוּ

such that the gezeira shava is between the bundle they use to paint the lintel in Egypt with the blood of the korban pesach.

Here I argue with the setama degemara in order to propose a different source for Rabbi Yehuda's din. Especially since some theorize that gezeira shava is just a mnemonic for an alternative but forgotten derasha, which is why ain adam dan gezeira shava leAtzmo. But even if it were not so, I am convinced it is so. The derasha is only based on this pasuk, in Vayikra 23:40:

מ  וּלְקַחְתֶּם לָכֶם בַּיּוֹם הָרִאשׁוֹן, פְּרִי עֵץ הָדָר כַּפֹּת תְּמָרִים, וַעֲנַף עֵץ-עָבֹת, וְעַרְבֵי-נָחַל; וּשְׂמַחְתֶּם, לִפְנֵי ה אֱלֹהֵיכֶם--שִׁבְעַת יָמִים.

40 And ye shall take you on the first day the fruit of goodly trees, branches of palm-trees, and boughs of thick trees, and willows of the brook, and ye shall rejoice before the LORD your God seven days.

And more specifically, on the word כַּפֹּת. Immediately above it is translated as "branches".

However, the word also כַּפֹּת means a bundle tied together. Thus, to look in Jastrow for convenience, pg 662-663:

Thus, we have a derasha that the lulav and other species need to be in a bundle. And now we see why the esrog does not need to be in the bundle, וּלְקַחְתֶּם even though the word starts the pasuk:

מ  וּלְקַחְתֶּם לָכֶם בַּיּוֹם הָרִאשׁוֹן, פְּרִי עֵץ הָדָר כַּפֹּת תְּמָרִים, וַעֲנַף עֵץ-עָבֹת, וְעַרְבֵי-נָחַל; וּשְׂמַחְתֶּם, לִפְנֵי ה אֱלֹהֵיכֶם--שִׁבְעַת יָמִים.

40 And ye shall take you on the first day the fruit of goodly trees, branches of palm-trees, and boughs of thick trees, and willows of the brook, and ye shall rejoice before the LORD your God seven days.

It is because the bundle is only כַּפֹּת תְּמָרִים, וַעֲנַף עֵץ-עָבֹת, וְעַרְבֵי-נָחַל.

What about the Chachamim? We can say that they simply don't make the same derasha on the word kapot.

There is perhaps a further argument between Rabbi Meir and Rabbi Yehuda, in which they agree that the lulav requires an egged but differ in what species may be used. The Mishna on Succah 36b:

מתני' אין אוגדין את הלולב אלא במינו דברי רבי יהודה רבי מאיר אומר אפי' בחוט במשיחה אמר רבי מאיר מעשה באנשי ירושלים שהיו אוגדין את לולביהן בגימוניות של זהב אמרו לו במינו היו אוגדין אותו מלמטה:

THE LULAB22 MAY BE BOUND ONLY WITH [STRANDS OF] ITS OWN SPECIES; SO R. JUDAH. R. MEIR SAYS IT MAY BE BOUND EVEN WITH A CORD.23 R. MEIR OBSERVED, IT ACTUALLY OCCURRED THAT THE MEN24 OF JERUSALEM USED TO BIND THEIR LULABS WITH STRANDS OF GOLD. THEY25 ANSWERED HIM, BUT THEY BOUND IT WITH [STRANDS OF] ITS OWN SPECIES UNDERNEATH [THE STRANDS OF GOLD].26

Perhaps we can say that Rabbi Meir even agrees to the derasha on כַּפֹּת, but holds that it merely needs to be a כַּפֹּת, a binding, of the species mentioned in the pasuk. Meanwhile, Rabbi Yehuda holds that the כַּפֹּת needs to be a כַּפֹּת תְּמָרִים, that is a binding made out of palm tree.

This is then what Rava says in the gemara:

גמ' אמר רבא אפי' בסיב אפי' בעיקרא דדיקלא

Raba stated, A lulab may be bound even with bast, or even with [strips of] the roots of the date-palm.

Bast is the fibrous substance of the palm tree, used for making ropes. And the strips of the roots of a palm tree are also from the palm tree.

Of course, here we would end up arguing with Rava, and Amora, as to the meaning of this dispute. Because he also says that the dispute between Rabbi Yehuda and Rabbi Meir is the same as the dispute between Rabbi Yehuda and the Chachamim in the brayta, over whether lulav requires an egged.

Thus:

ואמר רבא מ"ט דרבי יהודה קסבר לולב צריך אגד ואי מייתי מינא אחרינא הוה חמשה מיני 

Raba further stated, What is the reason of R. Judah? He is of the opinion that the lulab22 must be bound so that if one uses another species, the wreath would contain five species.27

I am comfortable arguing with Rava here and saying that this is really a dispute in how to interpret the pasuk.

Would there be halachic implications if both Rabbi Meir and Rabbi Yehuda agree with each other and argue with the Chachamim, and maintain that an egged is required?