Use of the opening roll for corny/pointless exposition?

The general term for this is exposition, and TVTropes gives a long list of ways it's been achieved in film and fiction (covering the methods you describe, and many more); the expositions that appear at the beginning of a work are usually qualified with "opening", as in "Opening Narration", "Opening Monologue" (your On Poppy Hill examples), or "Opening Scroll" (as in Star Wars).

That said, not all such introductory exposition is qualified with "opening"; the classic "pull down the map" trope is known as "The Big Board", and letting the scene speak for itself (as with the girl mysteriously doing chores alone) is known as "mise en scene", and the static text overlay you're primarily asking is simply known as a "title card" (or intertitle).

The difference between these latter modes of exposition and the former, which precludes them being qualified with "opening", is they can appear anywhere in the film where exposition is needed, not just at the very start.

George Lucas called it a rollup.

Hampton Fancher and David Peoples Blade Runner didn't call it anything.

Peoples (the original screenwriter for Blade Runner, and who wrote the screenplay for Unforgiven) referred to the stills expositions in the script (which is full of technical information) for Unforgiven as crawl

A Glossary Of Screenwriting Terms & Filmmaking Definitions calls both types (still and moving) a crawl.

CRAWL
This is a term used for superimposed titles or text intended to move across/up/down/diagonally on screen. For example, the text at the beginning of Star Wars movies "Crawls" up into infinity. Or, the written words "(crawl)" in Unforgiven.

So, I guess the disappointing answer is: a crawl.

Edited to add: the opening exposition in Blade Runner is, technically, a crawl.