Why doesn't pgstat_report_analyze() focus on not-all-visible-page dead tuple counts, specifically?

I wonder why we're counting the number of dead tuples (or LP_DEAD stub
items) in the relation as a whole in ANALYZE's acquire_sample_rows()
function. Wouldn't it make more sense to focus on the "live vs dead
tuple properties" of heap pages that are not known to be all-visible
when we generate statistics for our pgstat_report_analyze() report?
These statistic collector stats are only for the benefit of autovacuum
scheduling -- and so they're *consumed* in a way that is totally
different to the nearby pg_statistic stats.

There is no good reason for the pgstat_report_analyze() stats to be
based on the same pg_class.relpages "denominator" as the pg_statistic
stats (it's just slightly easier to do it that way in
acquire_sample_rows(), I suppose). On the other hand, an alternative
behavior involving counting totaldeadrows against sampled
not-all-visible pages (but not otherwise) has a big benefit: doing so
would remove any risk that older/earlier PageIsAllVisible() pages will
bias ANALYZE in the direction of underestimating the count. This isn't
a theoretical benefit -- I have tied it to an issue with the
BenchmarkSQL TPC-C implementation [1].

This approach just seems natural to me. VACUUM intrinsically only
expects dead tuples/line pointers in not-all-visible pages. So
PageIsAllVisible() pages should not be counted here -- they are simply
irrelevant, because these stats are for autovacuum, and autovacuum
thinks they're irrelevant. What's more, VACUUM currently uses
vac_estimate_reltuples() to compensate for the fact that it skips some
pages using the visibility map -- pgstat_report_vacuum() expects a
whole-relation estimate. But if
pgstat_report_vacuum()/pgstat_report_analyze() expected statistics
about the general properties of live vs dead tuples (or LP_DEAD items)
on not-all-visible pages in the first place, then we wouldn't need to
compensate like this.

This new approach also buys us the ability to extrapolate a new
estimated number of dead tuples using old, stale stats. The stats can
be combined with the authoritative/known number of not-all-visible
pages right this second, since it's cheap enough to *accurately*
determine the total number of not-all-visible pages for a heap
relation by calling visibilitymap_count(). My guess is that this would
be much more accurate in practice: provided the original average
number of dead/live tuples (tuples per not-all-visible block) was
still reasonably accurate, the extrapolated "total dead tuples right
now" values would also be accurate.

I'm glossing over some obvious wrinkles here, such as: what happens to
totaldeadrows when 100% of all the pages ANALYZE samples are
PageIsAllVisible() pages? I think that it shouldn't be too hard to
come up with solutions to those problems (the extrapolation idea
already hints at a solution), but for now I'd like to keep the
discussion high level.

[1] https://postgr.es/m/CAH2-Wz=9R83wcwZcPUH4FVPeDM4znzbzMvp3rt21+XhQWMU8+g@mail.gmail.com
--
Peter Geoghegan