I don't think I said or implied anything about constant or variable speed. I said torque output is responsible for angular acceleration and the resultant power draw to infinity is the result of the motor attempting to make an infitesimal amount of more torque. If torque is not produced, there can be no acceleration or resultant speed change. It will continue to run at that speed, practically speaking.
As for your previous question, I repeat, "Looking from the system viewpoint if viscosity increases and system doesn't change (no control valve), the DP would normally go up, right? ".
RIGHT!
From the "pipe" point of view, the pressure differential at the pipe inlet to the pipe outlet must go up to move the same flowrate and you are indeed 100% right.
From the "pump" point of view, the differential head decreases, given that the density of both of the fluids remain equal and that the pump suction pressure is held constant, so the discharge pressure of the pump goes down.
Both of those, from a "system" point of view, decrease flow.
As for motors, just take a look at the motor torque output vs speed, and realize,
1.) That angular acceleration is a product of torque which is the product of two real things in this world, force and distance,
2.) Torque is not the result of power applied. Power is not a real force in this world. Energy is real. Power is the rate that energy is spent and, as such, is only a concept of the human mind. If you didn't have a watch, you would have no way to measure power or even a concept of power is. As far as I know, Mother Nature does not own a watch and She only lives in the present. She has no memory of what happened during the last second that passed, and neither does energy.
3.) Power is the measurement of how fast torque is applied.
Realizing these, you will understand my answer.