Controlnovice;
Just a practical observation, before we all jump in technical definitions. The term "load" refers more often
to the current than the kW among the facilties personnel in plants.
You did not meniton the purpose of watching the "load" on the motor. If it is to monitor energy consumption than you are right, kW is more useful.
On the other hand if someone wants to keep an eye on the motor to see that it is not overloaded, its the acutal current (amps) that matters. The thermal capacity of the the motor winding is limited by how much current it draws and not really on kW. If there are power factor correcting caps are involved, things get little more complicated. But that is a separate discussion.
Also for a given set up and within certain range, the current will vary approximately in proportion to change in the mechanical load it is driving. So it will be helpful if you post the purpose of monitoring the 'load'.
Plus it is much easier and cheaper to monitor the current only, if it serves the purpose, than kW.