>"Storing the mapping on a large device doesn't make sense" - I agree about this, the large device being a bulky host computer.

Strawman. The large device is the keyboard you need to lug around. Tell me, is your keyboard designed for use with a computer?

>Various OSes have various (sometimes quite severe) limitations regarding remapping and the "script" that you mention is also OS-specific which is a pain if you use multiple OSes.

No. It isn't a pain, it called hacking and you only need to do it once and it is free and shareable. So in this sense only one person has to do it once and it just works for everyone else from then on.