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You can make it happen by this way:
So, if user changes his mind, he should click "Choose File" again and choose nothing. At last user should click the "Cancel" button.
You've an alternative widget, if you wish to use: Drag and Drop Upload.
So you can serve more optional upload form to your user.
Users can remove their uploaded files easily. But this widget also allows to multiple upload. Therefore I'm not sure that widget is helpful for you.
If the files extensions are jpeg, png etc. which you want from the users, you can also use this widget. Here is our result:
I can say in conclusion, you can get rid of needless file by applying 1st. way, if you need files except for images.
I hope, it helps.
In addition to this, I'm escalating this issue to our developers as a feature request.
I cannot promise you it will surely implemented or not. However you'll be notified via this thread, if this feature is released.
But it's not implemented absolutely.