The Radak (Sefer HaMichlol, introduction) writes that Loshon HaKodesh is all but forgotten to us, and all we have left is what is in Tanach.
Modern Hebrew is not different than Turkish or Farsi – it is the language of a secular culture complete with all those things that we want to stay away from. The fact that some of those who speak Modern Hebrew are religious Jews is not different than the language of any country Jews are in where they speak the language of the land. The point is to stay away from the language of the land and only talk the language of the Jew.
The Chasam Sofer notes that while Chazal used many words and phrases borrowed from the Greeks and Romans, they never coined a new word, as has been done in modern hebrew, for in their holy opinion it was preferable to use other languages rather than create even a single new word that did not have its like, its example, in the Torah, since it could not be rooted in sanctity.
The Chasam Sofer EH 2:11 says that in ancient times Jews used to use a modified version of the non-Jewish languages for everyday (divrei chol) talk, similar to what Yiddish is. The Kuzari writes that Avrohom Avinu, therefore, spoke 2 different languages. One for holy speech – that was Loshon HaKodesh, and the other for mundane speech – that, the Kuzari says was some non-Jewish language that Avrohom Avinu took and changed around a little on his own. And thats the idea behind Yiddish. It is a non-Jewish language that we took and twisted a bit in order to make it exclusive among us.
The Rambam writes that even in the days of Ezra they had a translator to explain the Torah readings to the people – clearly, they did not speak Loshon Hakodesh, even before the Churban.