[DuncanWaring]

Does it make sense to you that an object that hasn’t changed its mass becomes more powerful the faster it goes when it is only powered by a constant power source?

It makes splendid sense.

One horsepower is 550 ft-lbs per second.

If your vehicle thruster produces one pound of thrust and the vehicle is not moving, it produces 0 horsepower. If it's moving at a rate of one foot per second, it has 1/550 horsepower. At 550 fps it's producing one horsepower, at 5500 fps it's producing ten horsepower.

Your understanding of the difference between "power" and "thrust" is a little weak.

[burzum]

Your handwaving about the conservation of energy is unconvincing. Are you honestly trying to tell me that the work done per unit time of a rocket increases with its velocity? The energy for that work has to come from somewhere. This implies that the chemical reactions and fuel use by the rocket increases with its velocity as well (and don’t try to bring up mass lost because if you increase your speed ten fold, you increase your kinetic energy a hundred fold while your mass might only drop by a small amount). Is this what you are trying to say?