It doesn’t necessarily, it’s just that most people not only have limited time to dedicate to supplemental physical conditioning/preparation work and also aren’t starting from a perfectly balanced athletic foundation.
In your case, you already had the flexibility, accuracy, coordination, and other athletic requisites to throw those kicks. So, yes, adding significant strength while continuing to train the other attributes would likely lead to a noticeable increase in power.
Really, regardless of what form the resistance takes all types are simply about challenging the body’s neuromuscular system. You can absolutely take elements from all the different variations on types of resistance training and put them into your physical preparation/conditioning program. My reasoning for putting Bodyweight as the most carry over is due to the multi-athletic attribute focus, total body coordination, core strength, dynamic stability/balance, and “three dimensional” strength built with exercises like Hollow Back Presses, Planche Push-Ups, Front Lever Rows, Human Flag variation, Single Leg Squats/Pistols, Strict Muscle-Ups, and even more so more advanced Ring Strength elements.
But, again, all other types of resistance training can be useful if they serve your needs, don’t throw your athletic qualities out of balance, and are readily available (so you can do them chronically/regularly enough to convince your body to adapt to them/supercompensate).