A, elevator support for people includes support for objects, so the sum of the work done by elevator support for people and the work done by gravity for people and objects is equal to the increase of kinetic energy of people and objects, so A is wrong;

B, the theorem of kinetic energy is quickly applied to things. The sum of the work done by people's support to the wooden box and the work done by gravity to the wooden box is equal to the increase of kinetic energy of the wooden box, so B is correct;

C, as can be seen from P=Fv, F is constant and the speed is increasing, so P is increasing, so C is correct;

D, as can be seen from P=Fv, F is constant and the speed is increasing, so P is increasing, so D is wrong.

Therefore: BC