We say Shema Yaavirena Daled Amos Birshus Harabim by Shofar.
Why don't we say that if there's an Eiruv you can. Lots of people would answer Loi Ploog, we don't want it to be that in Adelaide you don't blow Shofar and in Melbourne you do. If you want to answer that how come they said if you have a Beis Din you do blow Shofar. They should have said Loi Plug there If you don't it will be that in Yerushalayim you do blow Shofar and in Tel Aviv you don't?
Let us analyze Rabah's Gezeirah. He was worried about carrying four Amos in Reshus ha'Rabim (see Tosfos 29b, DH "Shema"). An Eiruv cannot be made for a Reshus ha'Rabim, only for a Karmelis. Rabah was surely aware that many other places did not have the Halachic status of a Reshus ha'Rabim, and yet applied his Gezeirah across the board. The root of the Gezeirah is that maintaining the Mitzvah of Shofar on Shabbos would have people picking up and carrying a Shofar, possibly in a Reshus ha'Rabim. However, the Ritva explains that the Gezeirah of Rabah did not apply when people would hear Shofar from a Beis Din, as only one person would blow for everyone and that would be arranged by the Beis Din in the presence of the Beis Din. Being that no one in the world would pick up a Shofar in Reshus ha'Rabim on Shabbos in order to fulfill the Mitzvah (as the Beis Din was the only one involved in the Mitzvah), there was no problem instituting that a Beis Din should blow Shofar.
All the best,
Yaakov Montrose