I believe the only upside is that site framing (headers, navbars, side menus, etc etc) doesn't flicker or jump around reflowing as you navigate across pages. Which is I think why almost every "webapp" out there does this - to provide visually continuous experience, even if this client-side intra-screen navigation is slower.

Surely, on a fast-enough connections this flicker is essentially invisible, but if your connection is far from perfect (crappy hotel WiFi or poor cellular reception), it is certainly well noticeable.

Also, it's easier to persist some state across the navigations. Like making it trivial for those (annoying) on-page support chat overlays not losing message history.

This rationale only applies to web "apps", not documents, of course.