Doing some quick math, if your bike is using 3kw to climb a reasonably steep (15% grade) hill at 8mph, we can calculate the weight it must be carrying, which ends up being about 1,200lbs
To answer your question, the limit on motor power exists as a proxy for limiting the weight, speed, and acceleration of ebikes within safe limits, since having an ebike charging uphill at 20mph with 500lbs of payload would present actual safety risks. Trying to regulate payload/speed/slope combinations directly has practical problems (police officers don't really want to stop delivery drivers to weight their cargo), while regulating motor power is much simpler.
To answer your question, the limit on motor power exists as a proxy for limiting the weight, speed, and acceleration of ebikes within safe limits, since having an ebike charging uphill at 20mph with 500lbs of payload would present actual safety risks. Trying to regulate payload/speed/slope combinations directly has practical problems (police officers don't really want to stop delivery drivers to weight their cargo), while regulating motor power is much simpler.