Cutting from timeline and placing clips into bin doesn't work

I think as @R Neil Haugen says, you need to generate Subclips to put in a folder

Edit the clip on timeline to what you need then hold CTRL down (on PC) and drag that into your subclips folder in your project panel

The icon changes to distinguish it from normal clip

I think it is CMD on a Mac? but I am not a Mac user.

You can also trim clips in Source Monitor, right click and choose create Subclip that way to generate it - and you can name these Subclips as you want.

The original Source Clips in Project Panel are not changed.

This video below is quite a good intro on Subclips. 

I like VideoRevealed Premiere tutorial Videos as they  straight down to the topic in a logical and clear manner

https://www.youtube.com/watch?v=IrPIDDF_8QA

This is quite an old Video tutorial but assume there are no recent changes.

I learned something myself here today 🙂

When dragging a trimmed clip from the timeline into the Project window, you are actually cloning the source clip.

Are you creating subclips? As that would be I think what you want to do.

<<Some of them are actually clips that I intentionally cut>>

It seems like you would want the section of the clip that you cut. Not the whole clip, otherwise, drop in the whole clip.

?