I’m having trouble comprehending some of your sentences (there’s some running on going on). So I don’t understand what you mean by “waiting for advanced search” - is that better or worse in the multi page world? I think it’s worse. With an SPA, all of the UI navigation can happen on the client, which is as quick as possible (no server round trip). The actual searching in an SPA would be via an API and you get a nice spinner in the meantime, again with no page load. All smooth UI transitions which indicate to the user what exactly is happening. No blank page while a new page is computed without knowing what exactly is going on.
What I was trying to get at was that there are lots of "optional extras" that seem to get loaded up front at the moment that would be better if they were progressively loaded.
I think you see that a lot with SPAs in a way that you didn't when JS was used to 'progressively enhance' sites rather than for all interactions.
I don't think it's a problem of SPAs by definition — you could engineer an SPA to progressively load what's needed, and make the first load very slimline & then only load additional features while idle or on request, which is why I think GMail is a bad example. For example, I've just tried logging into Gmail in a fresh Firefox window (no cache) that I set to throttle to a "regular 3G" connection speed in the browser. It took literally 30s to load (with one email in the inbox).
I'm always hazy on the term amortized, but my understanding of it was the opposite — in that, you should try to chunk up as much as possible. If you are using Gmail for a longer period, having to wait for functionality like advanced search or predictive typing is less annoying as the extra time you need to wait is a smaller portion of your session overall. Plus, these things may have lazy loaded by the time you come to use them.
On the other hand, if you just wanted to reference an email quickly — e.g. I often need to dip into email quickly, for example, if I've travelling and have booking confirmations / QR Codes / PNRs etc. in starred messages in the inbox — you'll notice any extra load time so much more.
So to me, feels preferrable to have as small as possible initial load time, then extra functionality progressively loaded in the background.
I do agree for something like Netflix for example that a 'big load up front' is probably preferrable. I'm 'in for the long haul' as I'm going to be watching something that's at least 30minutes up to a feature length film, so a few seconds extra load time is negligble.