"I'd also question whether every device sold by Samsung and the other "premium" Android developers you mention, could be considered "premium"."
Of course, they aren't. But one can deduce what has happened to sales of the high-end models from those manufacturers by comparing previous handset totals, and ASP (average selling price). Samsung has said that the S6 + S6 Edge sold about as many as last year's S5, which itself was a disappointment in sales compared to 2013's S4. ASPs have fallen (by my calculations from $350 in Q2 2014 to $317 in Q2 2015 for Samsung; from $331 to $319 for Sony; from $237 to $235 for LG [not much of a fall]; HTC from $388 to $237. Motorola/Lenovo isn't exactly comparable because it spans a takeover period.
(One can calculate the numbers from publicly available figures, but I can't point you to a specific place for them - I just looked them up.)
If ASPs are falling, then generally you can infer that fewer top-end phones are being sold. You can easily think up scenarios where that's not the case, but all the indicators are down: fewer phones, lower ASPs, lower revenues.
"Certainly there's a lot of Samsung devices that are aimed further downmarket than some of those from Xiaomi or Huawei (and vice versa)."
But that's always been the case, even before Xiaomi or Huawei were contenders. However before them, there were few choices for premium features as you can get cheaper from Xiaomi and Huawei and OnePlus and so on.
"And even within a single manufacturer, you've not presented any evidence to suggest that people haven't shifted from non-premium Samsung to premium Samsung."
I think you mean that the other way round? (From premium to non-premium.) I haven't presented that evidence because it's impossible to extract from the available data. You'd need a giant consumer panel, like that run by Kantar ComTech, to see those shifts. But we can say with clarity that the companies that used to define "premium Android" are selling fewer phones at the premium end - which is told through lower ASPs, revenues, handset sales and profits.
"(You could argue that would inevitably lead to higher profits, but I'm not sure that high profit is synonymous with "premium", so if that's the assumption then it's worth spelling out)."
Yes, it is generally my assumption - one I think is accepted more generally than just in smartphones - that premium products attract higher gross margins. Other things being equal, that should feed through to higher operating profits.