There's no reason you can't shove many optical fibers into that 5mm diameter. People don't, in short distance applications, to have simpler systems and connectors.
There's big reasons why we don't use power over fiber (the endpoints are very expensive, and the overall system efficiencies are low). None of them have to do with the highest optical power density you could hit.
If the design criteria for cables was "make a good cable", we wouldn't have thousands of different types. There are cables which have different mechanical and environmental properties, different cost constraints, prioritization of different performance characteristics, etc.
> Can you have a copper cable able to deliver power over a long distance but unable to deliver the same power over a shorter distance?
Depending on the particular application, yes. Consider some 12/2 solid Romex. It'll handle 10 watts just fine, for quite a distance, if you want. Won't work well for a 1 meter long phone charging cable, though. Different mechanical requirements.