When did this trend start ?
 

I’ve noticed a lot of modern movies often have these very long shots on which no one speaks and classical music is playing.

Either a character stares into the distance or you see rain falling or something like that.

When did this become such a popular trend in movies ?

Faux-emotion from a tried and tested technique :D
Modern movies suffer with bad writers... so when they need to actually write emotion, they can't... so they resort to the scene of just having the character standing silently watching their surroundings while sad music plays.
It's an easy out for modern writers to borrow from movies and stories of yesteryear rather than actually write anything.

Because not everybody is Ming-liang Tsai

https://youtu.be/q-FPs4CMXwU

I've got to agree with you there!

Re: When did this trend start ?
 

It's all driven by contempt for art and audiences. Here's your slop.