What I think....
My K5IIs is as good or better than a K3 at high ISO shooting, but out past 6400 it is just very "iffy". If you have decent light and just need more speed, you can go up to about 2500 with decent results...sometimes.
ISO 2500 F6.7 1/200 @500mm handheld.
12,800 is very chancy...
Squirrels can be shot with mediocre decency up to about 6400.....if the light is fair. Their texture hides a lot of noise.
ISO 6400 1/125 @ 500mm handheld
Overall, I find that 3200 is where you start to lose IQ in more noticeable ways than just noise. Colors and bleeding can occur, and detail is starting to fade.
I haven't found any noise reduction programs that don't also cause loss of detail, and they do nothing for the color problems of a very high ISO shot.
Of course, there are always shots that are exceptions and can be decent at very high ISO values, but I find them to be exceptions, not the rule.
If I have good light, and need more speed, this is where I find bumping the ISO works best. I believe that 51,200 is more likely to disappoint than not in most cases. It's just a fact of life I live with and shoot accordingly.
I expect the K1 to improve that for me to some extent, but I am not expecting any miracles. The lower you can keep the ISO on any camera, the more you are going to like the results. In some cases...flash may be the best alternative. Those that have mastered flash use can get very pleasing results without much worry. I'm not one of them, but wish I was!
Best Regards!