> But ROW values or composite types that "are null" are counted, anyway.
Well, there's nulls and nulls. The SQL "IS NULL" construct is fairly badly designed IMO, because it considers both a plain NULL and a row-of-all-NULL-fields to be "null". count(), like just about everything in Postgres other than "IS NULL", considers only a plain NULL to be null.
This is discussed somewhere in the manual, but I think it's under IS NULL, not under all the other places that'd have to be annotated if we decide to annotate as you're suggesting. (One example is that functions that are marked STRICT use the tighter interpretation.)
You could use "COUNT(*) FILTER (WHERE NOT (whatever IS NULL))" if you want to count values meeting the IS NULL definition. (Buttressing my point that IS NULL is not well thought out, the obvious "whatever IS NOT NULL" doesn't work here, because it's not the inverse of "whatever IS NULL".)
I am aware of the mess, and I feel your pain (and my own).
But count(<expression>) is among the most frequently used functions, and hardly any user reading the manual will be aware of the implications. Maybe just:
... in which the input value is not null (does not evaluate to a scalar NULL).