In my opinion this setting should be a global switch. Either all files are stripped from metadata or all have them. There’s no need for EXIF in thumbnails, but colour profiles are much needed.
For example, prior to optimization I had an issue with photography.szmigieldesign.pl where originals opened in lightbox had sRGB attached to them and they displayed correctly. However, images in slider were technically thumbnails and they were stripped from colour profiles which resulted in colour shift. One could see oversaturated image at first and had different original in lightbox.
I had to install a WP plugin that forces image conversion through imagick that retains metadata to counter this effect.
This problem doesn’t occur in Chrome as it falls back to sRGB when no profiles are found. However, Firefox saturates the hell out of images if there’s no profile attached. It can be changed in about:config, but it’s non-standard.
One problem that I see is that WordPress by default strips metadata from thumbnails if the processing isn’t done with external tool like imagick. So, for most users the option to retain metadata will apply only to originals anyway.