The comments are hashing out some loopholes in the discussion (which provide some valuable insight), but trying to take the question at more-or-less face value
1. Standing armies become far less important
In a world where literally everyone has effective mastery over the viable military form, standing armies aren't nearly as important. Already in many historic societies large armies were only formed when needed, but now with literally no need of combat training, creating armies in times of need is far, far easier and faster.
2. Guerilla warfare is the defacto standard
...Further, when any house spouse, child, farmer, craftsman, noble... can join in battle, controlling the populace is near impossible. Any people you attempt to subdue are capable of taking your troops on. This is a huge problem for actually conquering an enemy, and it becomes an extremely powerful tool for the defending nation, tribe, or people.
3. Logistics and strategy will outweigh tactics
Assuming your only real force in combat are some variation of martial artists, intelligent commanders will need to figure out some way to create an edge. After all, everyone has troops composed of hundreds of men (and women?) who have mastered multiple forms of warfare. They'll start exploring means outside of the martial arts to empower their forces. Supply lines? Dragoon-style forces? Troop distribution? Whatever they can find.
4. Large armies will be far harder to maintain
Speaking of supply lines, most historic societies had trouble with them. Instead many resulted to pillaging the lands they moved through simply in order to support their troops. Since every farmer and shepherd can defend their own land, making forced acquisition costly... well... this causes problems.
5. Troops will be allowed to do their own thing (more than they were previously)
Assuming that the mastery of various martial arts comes with the theory behind them, your troops will understand the "why" and "how" of the forms, movements, and practices that compose the martial arts; they'll understand the theories that drive the function. This will allow them to have a tactical understanding in the midst of battle far, far better your average joe holding a spear.
In ye olde times organization and command of troops was already difficult (those societies who figured out methods of command and organization through, say, trumpet calls and tight, well practiced formations are generally highlighted in history books), so self-sufficient and self-empowered units is faster, more dynamic, and simply... easier. Unless a civilization has already pioneered advanced military command and organization tactics, this is an easy win. Some level of localized command during battle will be maintained, but for ho-hum kingdom without much knowledge of warfare hands-off will be the best approach.