I wrote:

You didn't quote what you were responding to,
but I assume it was the quote of mine above.
Actually, what i wrote is correct.  David Dyer-Bennet
wrote something similar.  The circle of confusion
is the acceptable blur and it makes sense to talk
about this in terms of enlargement.  Something
that is acceptably sharp in an 8x enlargement may
not be acceptably sharp in a 20x enlargement.
In other words, your judgement of what's in focus
on the film depends on how big you plan to blow
it up.

Suppose I photograph the same scene with three
cameras: a digital P&S with a 6x8mm sensor,
35mm film cropped to 24x30mm, and 6x7 (really
about 56x70mm).  Then I make an 8x10 inch print
from each.  I have to enlarge them about 32x, 8x,
and 3.6x respectively.

A print is often considered acceptably sharp if it
has resolution around 4 line pairs/mm.  Let's say
this corresponds to a blur circle of 0.25mm - any
point blurred more than that starts to look soft.
Divide by the enlargement factor to get the acceptable
circle of confusion on the sensor/film.  It is
0.008mm, 0.03mm, and 0.07mm respectively.
(You can see that small format digi-P&Ses have to have
great image quality to make acceptable enlargements.)

In fact 0.03mm is about the C-o-C number that
most 35mm lens makers assumed when engraving
their DoF scales on lenses, back when all lenses
had DoF scales and there was no question of
mounting the lenses on a crop factor camera because
they didn't exist yet.  (You can check this for a lens
by computing C-o-C: c = f^2/N/H, where f=focal length,
N is f/number and H is hyperfocal distance.)

If I mount the 35mm lens on a 1.5x crop factor camera
and enlarge the image 12x to make my 8x10 print, the
acceptable C-o-C on the film has shrunk to 0.02mm.
The DoF scale on the lens will be too permissive.

On DoF: the hyperfocal distance is H = f^2/N/c.  Focusing at
H means a point at infinity is blurred to the size of the C-o-C.
This formula helps explains why larger formats have
less DoF at the same perspective.  To keep perspective
the same, focal length f scales up proportional to the
format size.  C-o-C also scales up.  But the formula has
two powers of f divided by one of c, so keeping f/number
constant, H goes up for larger formats.

None of this is really controversial.  There used to be a
"Lens FAQ" written by David Jacobson that summarized
DoF and other issues for the rec.photo groups, but I haven't
seen anyone refer to it in a long while.

CoC are the limt of OOF blur circles from a point that are considered
"in focus".  A point at the exact focal distance will image as a point
on the film, anything closer or farther away will image as a circle,
the size depending on how far from the plane of focus and which side
of it they are on.  Eventually, the circle gets big enough that people
start noticing the image is out of focus.

I messed up that whole thing. It seems one can just use the 1.5
multiplier to find comparable DOF. So it really is just exactly like
cropping.

Not anymore.  The fastest was Olympus's f1.8 that was on the C-series
of cameras
made between 2000 and 2004.  Right now, f2 would be the fastest, on a
Sony I think.
This is not to say an f1 isn't possible.  The P&S cameras provide the
freedom to place
the rear element anywere right up to the sensor itself, unlike DSLRs.
But the cost to
produce a decent (it would have to be a zoom since no one would buy a
P&S without one)
zoom with the wide end being f1 or f1.2 would be great, even if the
sensor was small.

You mean something like the "Leica Digital-Modul-R" for the R8/R9?