Why does the UK CAA restart its page numbering with every new chapter of their CAP publications?
That's an artefact of a different era. Before computers were used to create documentation, updating large documents was difficult and expensive. People tried to reduce the workload by using chapter-page numbering. When you have to add pages to a book, chapter-page numbering allows you to replace one chapter instead of having to reprint the whole book.
Some organizations even supplied book updates as individual pages with a 'list of effective pages' so you could swap them out in your copy.
Nowadays there's no reason to keep doing this. Rebuilding a document (generate the TOC and crossreferences) is cheap, printing is cheap. You already noticed the big disadvantages of chapter-page numbering to the user.
Why they're still doing this? Inertia, probably.
How to reference them? Page 5-2 works, and if you want to be comprehensive, page 5-2 (PDF page 124).
(sorry, no references. Just lots of experience building large documents)