Being that many people carry on Shabbos due to established city - eruvim, why shouldn't they take the Lulav on Shabbos if they are already carrying their tallis and other objects?
The takanah of Rabbi Yochanan ben Zakai was made as a lo plug, no differentiation whether there was an eruv or not. Also, it is not just a matter of carrying with no eruv.this is discussed in Not Shaking the Lulav on Shabbat. As Rashi explains, if communities with an eruv start bringing the lulav to shul, they would be violating the takanah of Rabbi Yochanan ben Zakai and would actually be destroying the unity of klal Yisrael. We do not have a Sanhedrin that can rule to overturn this takkanah. Hopefully, bimheirah beyameinu, the mashiach will come, we will have a rebuilt Bais Hamikdash and we can then follow the rules specified in the talmud for bringing the lulav to the Bais Hamikdash.
Rabbi Yohanan ben Zakkai (a resident of the land of Israel) instituted, following the destruction of the Second Temple, that certain mitzvot, lulav among them, not be observed on the Shabbat. His concern was that one who is not knowledgeable in the required practice may carry a ritual object (in this case a lulav, but similar enactments were made for a shofar and a megillat Esther) in the public domain, which would be a torah-level desecration of the Shabbat. While a lulav is “muktzeh” nowadays on Shabbat, this is due to Rabbi Yohanan ben Zakkai’s decree (which rendered a lulav useless on Shabbat), and is not, as Louis mistakenly understands, the reason for the decree.
Since the decree was made to apply even if there was an eruv, the lulav is muktzah on Shabbos just like a shofar.
After the Talmud describes the different practices of Diaspora Jewry and those in Israel in regard to lulav, it continues with a separate, but related, topic, and then discusses the custom of waving a willow branch, which was instituted as a commemoration of a similar practice performed in the Temple during the Sukkot holiday. The discussion concludes that just as a willow was not waved in the Diaspora, the communities in Israel refrained from doing so as well. This seems to be in direct contrast to the practice of taking the lulav, where the communities in the Diaspora and the land of Israel had different practices. The Talmud admits that a mistake had been made with regard to lulav, and concludes that the communities of the land of Israel did indeed refrain from taking a lulav, even on the first day of the holiday.
Second, once the mistake has been corrected, it is clear that the Jews of Israel did not take the lulav on Shabbat. Rather, as noted above, they ceased this practice following the destruction of the Second Temple, at the behest of Rabbi Yohanan ben Zakkai, who lived in Israel. Thus, the practice in the land of Israel since the time of the destruction of the Second Temple seems to have been to refrain from taking the lulav on the first day of Sukkot if it coincides with Shabbat.
Finally, there is no imposition of any worldviews. The Jews of Babylon did not dictate that Jews in Israel should not take their lulavim on the first day of the holiday if it falls on Shabbat. Rather, it is clear from the language of the Talmud they merely described the existing reality.
Significantly, on this last point, Rashi (who is recognized as the premier contributor to Biblical and Talmudic exegesis, and whose comments are generally assumed to reflect the most straightforward understanding of a text) explains that the reason that the Jews of the land of Israel changed their practice was to prevent the breakdown of the Jewish people into separate groups – indeed to promote Jewish unity. This is consistent with the tone throughout the entire corpus of the Talmud, which describes the open lines of communication between the Jews of Babylonia and those living in the land of Israel, and in fact the respect and reverence shown by the former toward the latter.
An eruv is no better than one's own house. When Rav Yochanan ben Zakkai made the takana, he could have made it that everyone should take the lulav in their house before coming to shul.
But we see that he was concerned that there might be one person who needed help, and would thus leave his house to ask for help in a forbidden way. It's a far-fetched concern, but clearly Rav YbZ was extremely cautious about potential chillul Shabbos.
Thus even when most people live with an eruv, we are still concerned about that individual who would carry without one.
(Many of the people who lack a strong Jewish background, and thus would be likely to need to ask for help and be at risk for carrying, also live in small Jewish communities without eruvim.)
I remember seeing another answer- it was a long time ago and I don't remember the source or how reputable it is.
The suggestion is that Rav YbZ was extremely concerned that people should remember the beis hamikdosh. Therefore, he made "extreme" takonos which would reinforce this, and make sure we keep it in mind.
Thus, it's not just a question of "for the far-fetched chance that someone will break Shabbos to carry the lulav to ask how to take it, it's worth millions of Jews throughout the generations not fulfilling their mitzvah?"
It's also making sure that millions of Jews will remember the beis hamikdash and daven for Hashem to make us worthy of it.
That's actually the context of the gemara in Sukkah (and rosh hashana-same exact gemara.) The gemara say that the obligation to make "Zecher lamikdash" is from a verse "ein doresh lah"- the Jews are criticized since they are not "doresh" Zion, they don't seek it out. The gemara concludes that we see an obligation to "seek out" Zion, to make remembrances.