JPEG and RAW should be handled and displayed as a unit if both are present, otherwise JPEG should be used

If both RAW and associated JPEG are present at import, they should be displayed only once and be treated as one logical unit in file operations etc. However, if there only is a JPEG, the JPEG should be displayed.

Implementation Options

A quick workaround with minimal implementation effort may be to add in the Global Filters list "Always hide JPEG if RAW is present". That would not necessarily address the issues around deleting or moving files, but at least give a basic capability to handle both "JPEG only" and "JPEG+RAW" in the 

The import dialog already has the "Link JPEG and RAW" feature, but it currently only seems to apply to the file naming. I would also deem it very helpful if this feature would work for all existing pictures, not only for freshly imported ones. But that could also be resolved by a one-off conversion feature.

Rationale and drivers for urgency:

The RAW and the JPEG are two representations of the same picture. They should by default be displayed only once (and probably only have one catalog entry). If I delete the one thumbnail displayed for both of them, both files (and the XMP) should go to the bin. For any processing, C1 would typically use the RAW file if it is present. 

In the past, you could work around the issue by filtering out the JPEGs, because most people would shoot both. This workaround is not feasible anymore - even Pros use their mobiles (as a "sketch book", when it is not allowed to use a "proper" camera, or simply because it is the only camera on hand). You cannot assume that a photographer creates RAW files also on his mobile (until very recently, Samsung did not even allow that for all lenses). Every other RAW processor seems to work that way (at least Lightroom does for sure). Hence if C1 does not introduce a feature to show RAW and JPEG pictures without duplicates, there is a material risk that C1 becomes obsolete as it does not fit modern workflows and the development of mobile photography anymore.

There are other reasons for shooting both JPEG and RAW, such as long-term archiving (at the moment C1 can still read RAWs of my 20 year old D80, but I don't want to hold my breath for the next 30 years...).

I see that this feature has been requested several times. It is typically followed by  comments of some other users of the kind "real pros do not use JPEGs". I have explained above why it is critical in today's world to have this capability. There are also been some haggling on what exactly is the feature requested (whether pictures should be stacked or just shown only once). I think that's an implementation detail and best left to Capture One (I personally would prefer to see only one picture if both JPEG and RAW are present, but opinions may differ, so maybe configurability is the way to go).