Very well thought out arguments that I would agree with in general, though I
would add two unfortunate caveats below (unfortunate tricks played on us by
nature's penchant for recycling).

So some remarkable technological advances (automation, substantial reduction
in reaction scale, etc.) have resulted in the exponentially decreasing price
of gene sequencing.  There is at least some expectation that this trend will
continue, and so we can envision some time in the future where there will be
no cost prohibitiveness to sequencing entire genomes.  So shooting off
ambitiously into the future, lets say we've just reached the point where
we've sequenced the genome of every living species on Earth.  Given this
database (who knows, 10^8 to 10^14 total species of average size of 10^3 kb,
we'll definitely want a Macintosh for storage, along with software by the
next generation of Felsensteins), would it be possible to do complete
reconstructions of ancestral genomes at each node on the tree of life?

I would argue that this task is intractable, for two reasons.  The first is
basically the signal-to-noise problem; some genes have undergone significant
enough diversification since speciation that their ancestral states cannot
be reconstructed with any statistical robustness, even given a surplus of
information through sampling.  This is sometimes a problem when a protein
has changed function in one lineage versus another, and so falls outside of
the constraints of evolutionary models.  Some genes appear to be highly
'malleable', so that they may be prone to large insertions or deletions or
might have a high proportion of their amino acids free to change.  Protein
families undergoing rapid expansion are also problematic, such as Zn-finger
proteins in the human genome, so that every species has a different number
of copies, rendering insoluble the number of copies present in ancestral
genomes.

You could rightly argue here that we should be able to go back and just
resequence a vast number of different strains of a particular species.  This
is a certainly a good idea, but in cases where this has been done (with
microbial genomes), it has been evident without exception that genomes have
a substantial, rapidly evolving element.  Albeit frustrating, this is
something of a natural result of genetic drift, aka the bottleneck effect;
though we know with certain those magical "intermediate forms" must have
existed, they just weren't lucky enough to perpetuate their gene pool.

This brings up the second problem -- from which the signal-to-noise problem
really stems -- which is that of extinction.  Even if we've sampled the
genomes of every living thing on Earth, we know with certainty that we're
missing a substantial amount of data from extinct organisms.  Furthermore,
gene families undergo invention, expansion, diversification, and extinction
in a remarkably similar fashion as do species.  But with only a few rare
exceptions so far, genetic material is rapidly degraded outside of the
protective environment of the cell and so there exists no substantial
genetic fossil record to be excavated.  So again by analogy, given
morphological, anatomical, and physiological data for all living things,
would we be able to infer the existence of dinosaurs?

So back to the bottom line: it's absolutely feasible that entire families of
proteins have been invented in the past that have left no descendents in the
proteomes of any modern organisms.  These may have been involved in e.g.
optimizing light harvesting under a selectively attenuating organic haze on
the Archean Earth, or for scavenging metals in the sulfidic/reducing
environment of the early ocean, or for any other number of completely
speculative things.  But for whatever reason, these proteins represented an
evolutionary cul-de-sac whose usefullness was exhausted as times and
environments changed.

While we might be able to get a partially complete picture of ancestral
genomes and phenotypes, possibly even reconstruct these organisms via some
Venter-esque Frankengenome, there will undoubtedly be missing pieces.  What
has yet to be elucidated is how substantial these missing pieces will be,
and (more interestingly) if there remains to be discovered some underlying
rules or modularity in complex biological systems that will allow us to fill
in these gaps.
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