I think there are a number of ways the pagination could be improved. My suggestions get less complex as they go on, but start with my ideal and work down to what I'd be happy to settle with.
I commonly use the
<!--nextpage--> tag to split up long pages. In order to help readers, I usually also put an
<h3> header at the start of each sub-page (which means I then get a Title and a Subtitle at the start of Page 2, Page 3, etc, but I think that's helpful).
Anyway, what would be great is instead of having just "Pages: 1 2 3" at the foot of the page I could *also* have "Next:" and then the h3 subtitle from the start of the next subpage.
So on a page that's titled "Care of widgets" and where the second page has the subtitle "Washing your widget" I would have at the foot of page 1 not only "Pages: 1 2" but also (at the foot of the content) a link saying "Next: Washing your widget." This would be far more informative and inviting for readers, and would also be good SEO. I'm not quite sure how "Previous" links would work.
I'm clueless about php, so I don't know whether it would be feasible to take the first subtitle on a subpage and turn it into a link.
OR.. what would be a good second best would be to not only have the "Pages: 1 2 3" links but to automatically insert a link at the foot of each page (except the last) that says "Continued" and which links to the next page.
This is my least favorite suggestion, but still better than the default. Instead of having having "Pages 1 2 3" you could have "1 2 3 Next >" and "< Previous 1 2 3.
I think all of these would be an improvement on the default arrangement, which works fine but isn't very inviting to readers.