To me personally, the most important things when af-c is involved are:
1. the light available (with af-c you need fast shutter speed and if the light is not good, a lot of aditional work has to be done to get good results); and by good light I'm not talking about plenty of light
2. the settings used which can be quite different depending on the subject
3. the experience of the photographer when comes to shooting action; this is probably the most important aspect.
4. the distance between the photographer and the subject
I just got back from a vacation in Cote d'Azur - France. One day I had fun shooting seagulls on Monaco's harbour (I was the only one among the tourists who wasn't shooting the beautiful view; I'm really not a fan of landscapes, architecture, etc.) and there was a guy who came to me and ask me what the hell I'm doing with a 35mm lens on a full frame camera shooting seagulls that were flying fast to us (they were taking advantage of the strong wind in the harbour). He was also using a Canon (70D I think) and he had with him 5 L lenses just to be sure he can cover everything. I don't take more than 2 lenses in vacation and I always try to get the light ones. Anyway, he offered to give me his 100-400mmL lens to take some (let me quote him)
decent images of the seagulls.
I politely refused his offer by saying that I'm just trying to have fun, not to get National Geographic images.
He started to shoot seagulls next to me but soon after he start complaining about the af-c (Ai servo) of his camera. Given the fact that my wife went shopping (you guys know that we have all the time we need when our wifes goes shopping)
I gave him my camera (a 5D Mark IV) for 15-20 minutes to try it with his 100-400mmL lens. The results were the same as the ones he got with the 70D and he didn't understood why. I knew why.
He chosed the wrong settings, the wrong aproach, the wrong angle to shoot those birds. Guess what? He told me that I have to send my camera to a service and check it because it seems that it has issues with the focus.
I told him that when he will stop relying only on his camera and on his expensive L lenses he will start getting good images with any gear. And since he was sure that my camera is to blame for his poor results, I took some BIF images of the seagulls with the 35mm lens and then with my 70-200mm f4 lens just to avoid debating with him. I also used for a few shots his memory card so that he can study at home and pixel peep the images. He will also realise (aside the fact that my camera doesn't have focusing problem) that he can take good images of seagulls in flight with a 35mm lens mounted on a full frame camera.
What I'm trying to say is that:
1. I'm hoping that he will realise that blaming the camera or the lenses will not improve his skills or his images. This is valid for any photographer no matter what gear he uses.
2. For day by day use there isn't a camera these days that can't handle some ocassionaly sport, BIF.
3. Professional photographers will always use propper gear to get their work done and that's why you don't see them complaining on forums about having poor results because of the gear they use.
4. It's better to test before buying gear based on specs and charts and based on cancan reviews
To the OP: K1 and K1 II are not action cameras. The fact that these 2 cameras can track a dog running at you and get some decent results is just a bonus for a camera that is great at what it was designed for. My 5D Mark IV is not an action camera either. But it is great for what it was designed for: a workhorse camera. Yes, I have more chances at BIF than I may have with K1, but this "luxury" costs almost double the price of a K1 Mark II and despite of that it's still far away from 1Dx Mark II when comes to action. I know that if I want to stand a chance against a guy who uses a 1Dx Mark II or a D5, I have to work harder and I also know that there are times when I simply can't get a particular shot as good as they get with those action cameras. So, even if your findings regarding Pentax K1 Mark II af-c may be really good/valid ones (I don't know that because for example I never use 25 or 33 af points active in a situation like yours because grass tends to be a too much distraction for the af system), I'm certain that photographers interested mostly in action photography will not jump and buy K1 Mark II. Enjoy your camera because is a great one and keep posting your findings. I do learn from this kind of impressions a lot more than I'm learning from cancan articles written by DPReview and CO.