Just to offer a personal POV: I commuted on Armadillos for over a year,
and even rode a well-broken-in pair approx. 800 miles on my last tour,
all without a single puncture flat. I distinctly remember just giving a
little chuckle when I rode through a patch of broken glass on the road,
especially when riding in a group and watching the rest of them madly
swerve around it.
That being said, I no longer ride Armadillos, or indeed anything much
more puncture-resistant than the Panaracer T-Servs on my winter fixie,
because they make the bike feel like it's rolling along on garden
hoses, not tires. Worse, because the tires themselves are so rigid,
they're almost impossible to get a quick "squeeze" pressure read on, so
I probably went through just as many tubes from valve stem tear-outs
when uneccessarily topping off the pressure.
Also, the not-quite-round cross-section of the tire always made my bike
feel squirrely in corners. I've had a couple of crashes riding on
Armadillo 700Cx25 tires while attempting cornering that worked fine
with Michelin 700Cx23 rubber in equivalent conditions.
I've never used the liners or slime, but several people I know have as
a last-ditch attempt to avoid buying the new tires/rim tape/whatever
that really would have stopped them from constantly flatting. Of
course, proper inflation, regular checks of the rim for flaws, etc.,
all help a lot; even without armored tires, I haven't (knock on wood)
had a road flat in months.
Basically, it all comes down to just how hostile the environment you're
going to be riding in is, and how unwilling you are to ever stop and
fix a road flat. These days, I usually just carry my flat kit
regardless, and ride whatever tires were at hand (or on sale) the last
time I overhauled the bike.