I can't see much wrong with the expression myself. I think the reference
is to the sunshine (not cloud) being indistinct which is one of the
meanings of 'hazy' in my dictionary.
Why should an adjective in general use be restricted to descriptions of
visibility just because the noun is also used technically for one
visibility range/obscuration type?


The point is that "hazy sunshine" is a separate phenomenon from "milky"
or "watery" sunshine. It's yellowish sunshine in a dirty atmosphere and
simply has a different look and feel to it from sunshine partially obscured by
Ci. There need not be any cloud at all for there to be real "hazy sunshine"
though quite frequently there is Cu, the bases of which are yellow/brown and
the tops white. When you can easily look directly at the red globe of the sun
at an altitude of 5°, that's hazy sunshine.
I have even heard a forecast of "hazy sunshine" for a day when the sun
was going to be intermittently obscured by small/medium Cu. That is just
crass.
I suspect one reason we hear so much of this phrase is that many of
today's weather presenters have little feel for the weather (many obvious
instances of this) and the distinction between haze and high cloud simply does
not occur to them. Perhaps they've never noticed it, or perhaps they have, but
think such niceties are beyond the public. Have they ever thought that just a
smithereen of education could be a good thing? Dream on.

Tudor Hughes, Warlingham, Surrey.