Presumably this is about intellectual property claims.

If you get into legal issues around patents, being able to prove when you made notes on something could be important.

Signing and dating each page helps demonstrate that you've been taking notes at specific times.

Crossing out the areas of the page that you don't use helps in case you get accused of deliberately leaving blank space in your notebook so you can backfill it later on a page that you already signed and dated.

Of course, this is predicated on the idea that you use pen and paper for notes! All of my notes have been digital for over a decade at this point.

I saw one in a stationary catalog some years ago. It was exactly as you describe it.

There was space for a notary seal as well. I think the idea was to have it notarized once every so often so that the notary was affirming the date on the page, and that location of the X-ed out areas.

I thought this was a myth

I still have the bound, page-numbered notebook issued to me by Microsoft in the late 90s for this exact purpose, along with a lecture explaining the methodology above. (A rather misguided effort by an IP attorney who was apparently new to software…)

Still being sold:

https://www.amazon.com/BookFactory-Black-Inventors-Notebook-...

for example.

Notice some of the features: pages are sewn in, so it will be obvious if one is removed, tamper-evident archival paper, space to sign each page.

Paper documents I think still have the most standing as evidence.

This doesn't look like size for a full notary seal but space for a witness to sign. I suppose a notary could stamp it someplace.