Everytime I stand on the balls of my feet I can feel my entire feet tensing up and after awhile my entire lower body would tense up, which slows down my entire movement. As a result I feel that standing flat footed completely relaxed allows me to have higher mobility in the court. However, most players I meet and play with recommend using balls of feet as its faster to them. Could someone explain how this works?
You may stand on your complete feet, just remember that the weight of your body should not be weighed or rested on the feet, the core should hold up the weight when you are in any position on court. This way you stand steady and able to pounce on any shot from your position using the initial force from your core and not literally lift your foot first for every movement.
In order to stand on the "balls" of your feet, you simply need to shift your weight forwards such that your heels lift off the floor slightly. The goal in badminton is not be be literally on the balls of your feet, but not to have the weight in your heels.
In my opinion, the best is not to stand on the balls of the feet, but to do split step when your opponent hit the shuttle. In doing the split step, you go on your feet balls. As it is only a split moment, your body won't tense up.