Mark, I agree but disagree.
The main thing that I can consider is training specific per fighter and per style. In regards to running and kickboxing, sure its not that similar but a great place to start. The same muscles a sprinter uses (hip Flexors) are the same muscles we use to throw full speed and power into a kick. Endurance plays a big part in the sport and all the camps in Thailand that I have been to and trained in, had specific, long distance and duration runs. Again it is an individual thing and I keep stressing that. Road work is age old for fitness in any fighting sport, Thaiboxing not being an exception but an example. Because the human body functions under the control of our nervous system (brains) we need to stimulate our brains and thats one thing I feel people need to do. Run on different torrains, hills, times of day, weather, durations and pace. Some forms of power training plyometric, ballistic and power lifting can also aid in getting power in movements thats simple but I disagree with Thai boxers not utilising as much aerobic energy during a fight. Unless a fight ends in the first round I have not seen anyone that aint puffing after a fight.
Understanding and enhancing an individuals VO2max is crucial, not just for the fighter but his corner. I have seen many fights where the guy controls the first 4 rounds only to slow in the 5th and lose by KO or TKO. My belief is that aeorobic training for fighters is good but too much of a good thing is bad and I agree there too. Swimming is a great way to build endurance and it offers areas for fighters that running cannot. Breathing in swimming is a crucial thing and so is breathing with a mouth peice. Some people can run to heaven and back but with a mouth peice in, they are lucky to get to the local store.

So, back to it. I still stand by a mix of training to develop a full packaged athlete.