Another contradiction with that mathematics is that it shows no energy added to the rocket when its velocity is zero, because power is proportional to velocity. A mass would not be able to accelerate from zero velocity, if that were true. On top of that, velocity is relative. So the mass would be able to accelerate relative to some reference frames but not others, which of course is absurd. Since velocity is relative, the rate at which energy is added to either the rocket mass or exhaust mass varies with reference frames.
Physicist have no problem with that.
But when the velocity is zero, the whole concept falls apart, because then no energy is being added, yet acceleration occurs. A mass cannot accelerate without energy being added to it.