Likely not solvable until we have a BCI working.

People take ~150 ms to react and press a key, the ~400ms in running/walking is because you need to first shift your feet into a new orientation and let gravity change your momentum. The physical distance signals need to travel down the length of your spine, and the need to move your feet is larger distance before any change can occur etc.

Watch a sprinting football player dodge. Their feet go in the opposite direction as they want to move the same way you move an inverted pendulum. If you want the top of an inverted pendulum to move left you move your hand to the right. It still looks very fast because you don’t see the initial ~200ms delay between deciding to doge and the point when their feet start to respond.

Most martial arts will teach their own type of footwork optimized for the style, but it’s common to use a shuffling motion which keeps people’s feet close to the ground. It allows for a more rapid change in direction but is slower and less effective than normal walking if you actually want to get somewhere. Fencing and Kendo want more mobility where wrestling and Judo wants more stability etc.