Think of it this way. The control column acts as a potential(altitude) to kinetic (spd) energy converter. Pushing down increases kinetic energy and reduces potential energy and visa versa.
Thrust introduces more or less energy into that equation. All thing being equal increasing thrust, Firstly pushes the aircraft forward thereby increasing spd over the wing which in turn increases lift which changes the flight path of the aircraft(reduced ROD)
if the total energy (potential+kinetic) of the aircraft is correct but out of balance (low and fast or high and slow) then there is no need to adjust thrust . Simply use the flight controls to re distribute that energy.
if you rely on thrust to change flight path (to arrest ROD in flare) it will work however it will take slighty longer to achieve as you are relying on the secondary effect of adding thrust (similar to flying around and using the rudder to bank)