Because in Issur VeHetter, the Sanhedrin in Eretz Yisrael had authority over the Reish Galusa.
The Gemara says in Pesachim 51a
ורבה בר בר חנה לית ליה הא דתנן נותנין עליו חומרי המקום שיצא משם וחומרי המקום שהלך לשם אמר אביי הני מילי מבבל לבבל ומארץ ישראל לא"י אי נמי מבבל לא"י אבל מא"י לבבל לא כיון דאנן כייפינן להו עבדינן כוותייהו
The Gemara asks: And is Rabba bar bar Ḥana, who was lenient with regard to a matter that is prohibited, not in agreement with that which we learned in the mishna: When one travels from one place to another, the Sages impose upon him the stringencies of the place from which he left and the stringencies of the place to which he went? Abaye said: That applies when one travels from one place in Babylonia to another place in Babylonia, or from one place in Eretz Yisrael to another place in Eretz Yisrael, or alternatively, from Babylonia to Eretz Yisrael. However, when traveling from Eretz Yisrael to Babylonia, no, this principle does not apply. Since we, the residents of Babylonia, are subordinate to them in terms of halakha, we act in accordance with their custom, but a resident of Eretz Yisrael is not required to follow the Babylonian custom.
(Emphasis mine).
The reason is, as Rashi says:
אנן כייפינן לבני א"י דאינהו סמיכי ובבבל לא סמיכי
We're subject to those in Israel, since they have Smicha and we don't.
So the answer is that the Beis Din in Israel has authority since it has Smicha.
Tosfos says another answer:
בני א"י חכימי טפי דאוירא דא"י מחכים כדאמר הכא דאיקרו מחוקק שמלמדין תורה ברבים
The Torah scholars in Israel are wiser, since the air of Israel makes one wise, as the verse says "staff" - they teach Torah in public.
So why does the Reish Galusa have primacy in appointing judges?
Rashi says (on the Gemara you mentioned):
לשון שררה ויש להן רשות להפקיר דהפקר ב"ד הפקר דכתיב (עזרא י) וכל אשר לא יבא וגו' ביבמות בהאשה רבה
They have permission to declare objects owner-less, since the court has the power to make objects owner-less.