But what's the physical explanation for the behavior of these panels? Including when the load is a resistor, not a battery?
If these panels are rated for a max-power point of 17V 1.4A (24W), that would correspond to a load of 17/1.4 = 12 ohms. A load of 30 ohms, on a healthy panel, would accept about 18/30 = 0.6A or 11W. (I've added one volt there as a WAG for the rise in voltage due to the lesser load.) The measured output in this case was 5W, so about a half of that.
I have one conjecture: some of the cells have high internal resistance. That does not affect the open-circuit voltage. When a short circuit is applied, the section including the high-resistance cell(s) gets bypassed by bypass diode(s). That still allows the cells in the non-bypassed section(s) to output their full short-circuit current.
If that's the true explanation, then there should still be significant output into a low-enough resistance. If one half of the panel is bypassed, that should leave about 8 volts, which into a 30-ohm load would yield 0.26A or 2W. The reported output was actually higher than that. Perhaps 1/3 of the panel is bypassed, that should yield about 10.5V, or 0.35A (4W) into a 30 ohm load. Change that resistance to 8 ohms and the output would rise to 1.3A (14W).
In that case, like OH said, it's still OK to use as an "8V" panel (2/3 of its original "12V" nominal output), and putting two such panels in series, feeding a 12V battery via an MPPT controller, would yield about 60% of their promised wattage. Using a simpler controller, or wiring the 2-in-series pair in parallel with (paralleled singly) healthy panels, it would be more like 50% of their supposed wattage.