External power is for
- charging the battery (really silly to not implement that, because a charger is trivial, and if you charge slowly then it is really easy to incorporate that ... a few amps is a bit harder, hence all the problems with tablets overheating and shutting down when sun shines on them)
- time lapse shots e.g. taking pics of plants growing (people AFAIK use really old Canon cameras for that for which various remote control hacks have been developed)
- use as security cameras (AFAIK most of the temporary cameras on roadworks use high-end Canon DSLRs, somehow remotely connected)
Also, lithium cells last much longer when kept charged, so keeping a camera on a charger overnight will make the battery last much longer. I have found the various Pentax batteries last a year (of very low usage) and then this $50-$100 battery is scrap, and of course most of the ones on Ebay / Amazon are fakes. I have a Hahnel for the K3 and it is the 2nd one, and already it is about 50% capacity. The original Pentax one is better...
I agree that on a trip 2 batteries are better, but not when you find they are down to 20% of their published mAh (because they are 1 year old) and you didn't bring the charger
Can you use a dumb battery insert? Surely these batteries are chipped, so a K3 battery won't work in the K1 even if exactly the same dimensions and voltage (got this on the Canon G10 -> G40). The only way I see is to use the real battery and connect 2 wires to the actual cells, and supply 3.6V (or whatever the actual cell voltage is) so basically the battery never goes flat (even if the camera indicator says it is flat - not sure if that uses the voltage, or is integrating the current).
I can also see constructing a fake battery with a pickup coil, and doing induction charging, like modern phones. That is a really great feature... one of the best ever. But the fake battery would not have much room for the cells!