Power is explosive strength. Strength can't be expressed without resistance. We can train to get stronger and that will increase our power output, but how powerful one can be depends on one's genetic potential to explode. That's why olympic weightlifters are vetted and recruited based on their standing vertical jump. If you have an 18 inch vertical, no amount of training will increase it to 36 inches. Teams recruit those who are genetically powerful.
The best way for an athlete to train for general power is to do olympic lifts like the power clean. That in addition to training for power in patterns specific to your discipline yields tremendous results.
For my VT, the forms train our body mechanics for power generation like practicing power cleans with an unloaded bar, but to develop power specific to our discipline we use resistance from things like heavy bags and each other (
pun-sau) like training power cleans with a loaded bar.
Like the power clean, a power punch is generated from the ground up with relaxed arms. Once power is transferred from the lower body via the waist to the elbow, the entire body's strength is expressed explosively into the target. Therefore, general strength and power training are both essential.
For whatever reason, some lineages discourage weightlifting. I think that is terrible advice for a power athlete. Someone with a 200kg+ Clean and Jerk who also knows how to punch will take your head clean off your shoulders. Like this guy. That weight comes up fast as hell. That's incredible power (explosive strength). Channeled into a punch = oblivion!