My answer is not ultimately different to User-13249930999434776143’s. (Vote #1: User-13249930999434776143’s answer to Why is standard Albanian language based on the Tosk dialect and not the Gheg dialect?) But it is a bit less nuanced.
Albanian is divided into Tosk dialect in the south, and Geg dialect in the north.
The standard language of Albania before WWII was Southern Geg, based on the dialect of Elbasan. Elbasan Geg was close to the Tosk/Geg border, so it was a dialect that could serve as a middle point between Tosk and Geg. And while Elbasan was not the capital of the country, it was culturally prestigious. In other words, the choice of Elbasan Geg was a good choice of standard dialect, as these things go.
The postwar standard was not Southern Geg. It was Southern Tosk. So it was not a middle point of Tosk and Geg; it was at the extreme of dialects spoken within Albania. And it wasn’t spoken anywhere massively prestigious: it was spoken in places near the southern border of the country, like Vlorë and Korçë and Gjirokastër.
Postwar Albania was ruled by Enver Hoxha and his fellow partisans.
Enver Hoxha was born in?
That’s right. Gjirokastër.
It really is as simple as that.
By the time the communist regime fell, Southern Tosk had been entrenched in Albania as the standard language for a generation, and there was no move to restore the prewar standard. The most telling development for me was seeing Kosovo, which is Northern Geg, adopt Standard Albanian—based a dialect as far from the local dialect as you can get without ending up in the Arvanite diaspora. And Aziz Dida’s answer to my question Is there interest in keeping Geg as the standard language of Kosovo? shows, that has proven somewhat challenging for Kosovars.
EDIT: Death by standardization, a Gheg drama by User-13249930999434776143 on albanophilia. Drop everything, and read it.