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I kind of see what you're saying, but, if the girth hitch introduces more friction would it not be easier to load one leg more than the other? If you "cycle" a girth hitch enough you could create a situation like in this pic. If it were just an eye you couldn't...
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Your point about cycling is a good one, and your photo illustrates the point perfectly. If each cycle at the high point caused slippage to begin, and at the low point allowed the rope to become completely slack, then the splice should slowly walk apart over many cycles. But this would apply to a simple eye as well. Incidentally, my earlier point about the unequal distribution of forces on the two legs can be applied to your photo. If you were to hang a 10-lb weight from the slack leg in the photo, you would have to pull down on the other leg with somewhere between 800 and 2000 lbs in order to get the 10-lb weight to start moving up. A girth hitch makes a terrible pulley.
In the first photo I show a spliced eye in 3/16-inch Amsteel Blue that is girth-hitched to a link. This configuration could probably relax completely after each tension cycle, so it might creep apart if the bury were very short.
On the other hand, the girth hitch might undergo a permanent change under high tension so that all slippage would stop. The second photo shows the identical hitch with a much smaller eye. The "bridge" of the hitch still crosses both legs of the eye, but one leg is inside the other because the bridge is directly over the splice. Under heavy tension, the bridge creates a serious dent in the splice. Even better, the throat of the splice is not only under heavy tension but it is bent around the steel link. These two things together tend to lock up the splice and provide far greater holding power than the simple straight bury shown in the first photo. I haven't done experiments to prove it, but I suspect this configuration would be highly resistant to creep.
There are lots of twists and turns to this story--I bring it up just to remind people that a splice can't really be understood in isolation; how the eye is hooked up has a great deal to do with how the splice will perform.