This may be funny, but see also the /. news earlier this day: /./microsoft-to-teachers-using-pens-and-paper-not-fair-to-students

Cursive does teach motor skills in your hands, eye-to-hand coordination etc. And writing is still a basic skill that's needed in every job that requires discussing complex ideas with others.

On OP's question "What do students today realistically have to know to be successful in school?" I would say that the skills I see lacking are reading, writing and basic math. Especially the first one will get you anywhere you want...

Wow.

But they should have added a matchbox in the video, so that one can get a sense of scale...

I'm with you there.

Where I live (in the Netherlands), there is even a university that requires job applications to be submitted in either .doc or .docx. So, my nicely formatted .pdf (pdfLaTeX) goes into ImageMagick where it is converted to a sersies of .png. That is imported into LibroOffice and stored as .doc/x. Swallow that. Now, the files I submit are "only" 7.5 times bigger then necessary. Text cannot be selected anymore (by them), but that's their problem. And it didn't hurt: I was selected for interviews!