What is the purpose of the Sanhedrin if the Shulchan Aruch says that the public can decide laws based on the needs of the time? Doesnt a Sanhedrin and a rabbinical court in general in civil matters become completely obsolete?

ב"ה Shalom What I assume you are referring to is the concept of "Shivat Tovei Hair" which we can roughly translate "the seven (members) of the municipal council". The concept is basically a city governing council with the authority to make decisions on behalf of the Jewish community. It is dealt with extensively in the Talmudic encyclopedia in Hebrew in volume 19. There are indeed Rishonim who say that in absence of the Sanhedrin, their authority is like the authority of the Bet Din Hagadol.It is not , that the Sanhedrin becomes obsolete. To the contrary, it empowers the council with authority like the Sanhedrin in its absence. (שו"ת הרשב"א המיוחסות להרמב"ן סי' רפ, ועי"ש סי' נט וסי' סה, וכעי"ז בשו"ת הרשב"א ח"א סי' תשכט, הובא בסמ"ע חו"מ סי' ב ס"ק י, שכל ציבור במקומו כגאונים לכל ישראל שתיקנו כמה תקנות לכל ישראל. ועי' שו"ת הרשב"א שם סי' תשסט וח"ג סי' תיא ותיז וח"ד סי' קפה וח"ה סי' קכו; שו"ת ריב"ש סי' רמט ושצט). However, there are Rishonim who limit the authority to the Tovei Ha'ir and their opinions are summed up in the Rema to Choshen Mishpat 2. All the best