I wouldn't want the glue to fail when I needed those deck fittings in adverse conditions.

Better tell CLC then...
http://www.clcboats.com/shop/products/boat-building-supplies-epoxy-fiberglass-plywood/sailboat-rigging-hardware/carbon-eyestrap.html

If they are installed correctly they should not fail with the loads we place on them.

First if the epoxy has enough surface area to bond to there should be no failure. Most epoxies have a tensile strength between 5000 - 8000 PSI. Each mounting tab of the carbon pad eyes I make are about 3/8" square. That's a bonding area of about 0.28 SI. Assuming a lower strength epoxy (say 5000 psi) that works to an ideal pull strength of 1400 LBS. Even using a factor of safety of four that's still 350 LBS per pad eye. In case your wondering, the epoxy I use, Super Sap CLR/CLF, has a tensile strength of 9500 PSI.

What about at higher temperatures? Most of the epoxies we use have HDT (heat deflection temperatures where the epoxy STARTS to deform not lose strength) between 120 and 180 F. The ultimate failure temp is different and usually higher.

BTW: Don't glue them directly to the varnish. The varnish is the weakest layer. Urethanes are better but just. If you grind a patch into the base epoxy layers there should not be a bonding failure. Be sure to also roughen up the pad eye.

Commercially I've had ONE carbon fiber pad eye fail. The failure occurred in the pad eye itself. There were still flecks of carbon on the deck. If you use wooden pad eyes, the wood will fail before the epoxy used to bond it.

That said, I still prefer recessed fittings. Less likely you'll snag on one. They also look nice.