1) The simple answer is that if somebody knows how to perform these Mitzvos, he will do them wherever the Megilah, Shofar, or Lulav is located, so there is no worry that he will need to carry them. Rashi here (DH ha'Kol) writes that since a person is obligated to perform the Mitzvah, he is "Bahul" -- "over-eager" to do so. This is why there is a special worry that he will take the Mitzvah item to an expert to teach him how to do the Mitzvah. In contrast, if he knows how to do the Mitzvah and it is possible to do the Mitzvah where the item is located, he will not panic because he can easily go there in order to do the Mitzvah, so we do not need to be worried that he will violate a Torah prohibition in order to enable himself to do the Mitzvah.

2) There is a proof for the above explanation from the Tosfos ha'Rosh to Sukah 43b. The Gemara asks there why the Mitzvah of Aravah on Hoshanah Rabah in the Beis ha'Mikdash overrides Shabbos. Why is it not similar to Lulav which, because of the Gezeirah of Rabah, does not apply on Shabbos? The Tosfos ha'Rosh (DH Iy Hachi) explains the question of the Gemara to mean, why do we not make a Gezeirah lest he carry the Aravah in Reshus ha'Rabim? Since the Mitzvah of Aravah is performed in the courtyard of the Beis ha'Mikdash, why are we not concerned that he might carry the Aravah from his house to the courtyard of the Beis ha'Mikdash? One sees from this that if the Mitzvah must be performed in a specific place, a Gezeirah is indeed made so that he should not carry the object with the purpose of fulifilling the Mitzvah.

3) I saw the above source cited in the Hebrew edition of the ArtScroll Gemara, Sukah 43a, note 2 (DH Lich'orah). He also refers there to the Pnei Yehoshua at the very end of Maseches Sukah (DH Piska). The Pnei Yehoshua writes that if not for Rashi's explanation on Sukah 43b, he would have said that even for a Mitzvah where no special expertise is required, the Gezeirah of Rabah still applies. The reason why Rabah made a Gezeirah is that people might have thought that since the Megilah, Shofar, and Lulav are Mitzvos, it follows that they override Shabbos, so people might have thought that it is actually permitted by the Torah to carry them in Reshus ha'Rabim in order to do the Mitzvah. This would be why Rabah said that one should not do these Mitzvos on Shabbos because otherwise people might err and think that they are allowed l'Chatchilah to carry for this purpose.

4) The Pnei Yehoshua writes that according to this we can understand the reason why the Gemara says that the Gezeirah was made in order to prevent one from taking the Mitzvah item to an expert. This is merely a common reason applicable to Megilah, which is difficult to read properly, so there is more of a worry that one will take it to an expert to learn how to read precisely. However, the worry that one might carry the item in order to perform the Mitzvah should also be sufficient to justify the Gezeirah of Rabah.

Therefore, according to the Pnei Yehoshua, the answer to your question is that the Gemara mentions the reason of carrying for the purpose of learning because this is a common worry concerning the Mitzvah of Megilah, but carrying for the purpose of fulfilling the Mitzvah indeed is also a sufficient reason for Rabah to make his Gezeirah.

Kol Tuv,

Dovid Bloom