This annoys me as well. More so because the multiple monikers can confuse and alienate the classical neophyte. And also since I perform a number of classical pieces by modern asian composers for whom the written and spoken language is quite incomprehensible to most of my audience.
I think part of the origin goes back to Wanda Landowski and the rest of the historical performance crowd. If part of the goal was to perform a piece as Bach, or Haydn would have heard it, then it follows that everything else should as authentically original as possible as well. On the other hand (Most of us are not old enough to recall this) there was time in the lat 19th and early 20th century when it was the norm to not just translate the title of an opera, but the entire text as well. Perhaps our current endemic may be left over from that era.
When it comes to titles of pieces I think a more nuanced approach is appropriate. In America I live in a world of people, even among some classical connoisseurs, who mostly speak only English (or at least our americanized version of the language) to say to them "La Fille Du Regiment" would be meaningless. For other operas and pieces that have been ingrained in the repertoire I think it's fine to keep the original language, because that name retains its power to communicate.