As others have told you, there's something to say for both techniques and in the end we all use a blend of both. And practicing power-off landings is never a bad idea, as long as you have considerations for the engine (shock cooling) and the others in the circuit.
I think it's important not to focus on one or the other too much, but to understand some of the aerodynamics behind it.
First, what happens when you reduce the power to idle? Of course, thrust is reduced so you either maintain the pitch attitude and bleed off speed, or you have to lower the nose to keep the speed up. Trim plays a role here too. If the aircraft is trimmed correctly it will drop the nose by itself to maintain speed. But if the aircraft is not trimmed correctly you need to know exactly what control position/force is necessary to achieve the desired effect.
But that's not all. Due to propwash effects, p-factor and whatnot, reducing the power will induce yaw to the right (assuming the standard US Lycosaurus setup) which you need to counter with left rudder. For the exact same reasons that increasing the power, for instance at the startup roll, requires right rudder.
At your stage in training, do you find yourself intuitively controlling the rudder properly already so that the ball is centered? Or, in crosswind landings, can you keep the aircraft aligned with the runway intuitively while you play with the bank angle to induce a sideslip and maintain the centerline? Do you already know or feel the pitch attitude that's required to maintain speed with idle power, or to bleed off the correct amount of speed? If not, I can well imagine that your instructor is teaching you to land in stages, where you first reduce power to idle, have a second or so to consciously counter the yaw and pitch effects of this, and then start the flare.
And second, talking about the flare. This is not just a maneuver to bring up the nose so the nosewheel doesn't hit first. It's also a maneuver that's used to bleed off energy. After all, any movement of the controls, at any time, results in induced drag. But in the flare you are at the wrong end of the drag curve which multiplies this effect.
This is one of the two reasons we don't approach at stall speed. We need that extra energy for the flare. The steeper your approach is, the more energy you need. (The other reason is for protection against gusts.)
So again, your instructor will teach you to fly your final approach at a certain speed, and an approach angle that belongs to that speed. Eventually you should be able to fly to book (POH) numbers but initially your instructor may want you to fly a little faster than that. That gives you the ability to close the throttle a second or so before the flare, stabilize the aircraft again, maintain the pitch attitude so speed bleeds off, and still have enough energy left for the flare itself.
As you progress further, you'll fly the aircraft much more intuitively and you can combine all these actions. Heck, you could even extend the reasoning behind all this, and do something opposite if that's required. Pilot DAR has given you an example already: Leaving a bit of engine power on to prevent shock cooling. I'll give you another example. I was downwind 1000' in a fully loaded (4 adults) PA28 and needed to fly a tight circuit because of a 737 on final, which I had to get in front of (ATC orders). So I made a tight turn onto a tight final and approached the runway at a relatively high rate of descent. Instead of closing the throttle in the flare, I used a very small and short burst of power to cushion my ROD, and then made a very nice and controlled idle power touchdown. Without that burst of power I'm not sure if I would have gotten the energy to fully cushion the flare.