Richard, I am confused. If I had a Zone 1 and 2 annual Travelcard, and
converted it to Oyster, that would be vaild on National Rail within
those zones?

It would have the same validity on Oyster as on paper. No difference.

But not if I have an Oyster but buy 1-day Travelcards on
it?

You can't put one day travelcards on it.

Not only is that illogical but beyond my comprehension - why are
TOCs willing to accept one form of Oyster but not the other?

Because they have to accept the travelcards under their existing relationship
with London Underground but do not have to accept prepay unless they
decide to. And they have decided not to.

Or is the answer that they simply haven't (for whatever reason)
installed Oyster readers at all stations? And, if that is the reason,
then why doesn't the munificent Ken pay for them to be installed (at
our expense, no doubt)?

He has offered to pay for installation. They have still said no.