I guess it comes down to definitions and how 'full spectrum' is perceived.
Rightly or wrongly, I tend to think of it as a spectrum which contains the
same component colours in the same ratios, as natural daylight...

That's a reasonable definition for a video display, but it's not sufficient
for source lighting. It's difficult to make a "full spectrum" fluorescent
lamp, especially one that produces good color rendition for photograpy.


but I guess even that varies depending on filtering effects of cloud
cover and haze and so on. Even so, I'm sure that there must be some
definition of 'average spectrum daylight', and I would expect that any
display technology would aim to reproduce any colour in as closely
exact a way as it would appear if viewed directly under daylight.

The standard is D6500, a 6500K continuous spectrum from a black-body source.
What you suggest is, indeed, the intent.