Yes, I suspect you probably will!I guess I'm just going to have to remain confused!
I'm not really sure what 'rated at 6A' (in relation to a cordset) really means if it doesn't mean that it is deemed 'unsafe' for it to carry more than 6A, in which case, I would expect the required protective device to reflect that. Nor do I really understand why the 'CCCs' (the maximum current deemed to be 'safe') of a flexible cable of a given CSA should be appreciably different if it is part of an electrical installation or part of a moulded 'cordset' - indeed, if anything, I would expect the CCC (hence In of required protective device) to be lower for the latter, given the sort of treatment it might receive in service.
As I wrote earlier, a rating is a value assigned by a manufacturer. The manufacturers and regulatory bodies have sat around a table and reached a consensus about what protective device is appropriate and available for products dealt with in their standard. Similarly for BS1363 plugs. The same for those responsible for electrical installations. There is no reason why they should reach the same conclusions, and no reason why they should reach different conclusions. Of course their requirements will be broadly consistent, since "ye cannae change the laws of physics Jim", but you have to accept that each of those committees has access to empirical data and to basic safety standards, as well as knowing what is acceptable for their products.
I don't agree that CCC should be lower for cables likely to be subjected to rough treatment in service - the two things are not related. One might argue that the CCC of a cordset could be much greater than for the equivalent cable used as part of an installation, since it is unlikely to be installed in conduit, or bunched with other cables, and and tendency to overheat is likely to be noticed by the user.