Though I do generally agree with MJ, and support the idea that approaches are often flown with power, too fast. Pilots use power as a crutch in place of good technique power off. I do. I cannot completely agree with:
Stick some power on in the flare and you have a whole heap of energy to get rid of that the performance never catered for.
Yes, these words can be correct sometimes, but if you've got yourself behind the power curve, and you're dragging it in, your energy is already at a minimum, and you don't have much to loose. Some recent circuits I was flying in a Twin Otter with full flaps, reminded me of this. Certain planes just "feel better" carrying some power. I'm not saying that is right, but I agree that's the way it might feel.
If the student is using power in the flare to hone his technique, toward becoming skilled with power off flares, that's okay, as long as the end objective of good power off landings is not lost in laziness. I think that is better as a confidence building, learning aid, then a power off approach, during which a whole bunch of power is fed in at the last minute, in an attempt to fix a mess, and then you have a sudden configuration change on top of a poor flare, and still a mess. I was right seat to this in a 172 a few weeks back. Once the power was off, he should not have touched it, he just distracted himself, and forgot to fly the plane for a moment.
I had to familiarize myself in a Piper Navajo recently, after a two circuit checkout. Carrying power through the flare "felt better", but yes, at the expense of proper technique, and landing distances as described in the flight manual. (I had oodles of runway) I got myself to the point of confidence where power off was fine, but things in the flare happen faster.
Another thing I reminded myself during this type familiarizing exercise was that by carrying power, I was defeating an important human factors safety feature. For any retractable landplane, you'll probably have a gear warning horn, operated by reducing power to near idle with the gear up. If you don't reduce to idle, and the wheels were up, you wouldn't get the horn. If you'd forgotten the gear, the first and final reminder would be not good.
For those who do water landings, you will find that carrying power will give you better and safer landings. For floatplanes, a bounced landing can be much more serious much more quickly. Carrying power aids in precision, and not changing phases of flight too quickly, so you have time to optimize your technique. A safe power off glassy water landing would simply not be possible.
The applicable certification requirement is:
(1) Immediately prior to reaching the 50-foot altitude, a steady gliding approach shall have been maintained, with a true indicated air speed of at least 1.3 Vso.
(2) The landing shall be made in such a manner that there is no excessive vertical acceleration, no tendency to bounce, nose over, ground loop, porpoise, or water loop, and in such a manner that its reproduction shall not require any exceptional degree of skill on the part of the pilot or exceptionally favorable conditions.
Note "gliding" approach from 50 feet.
Perhaps like parallel parking, we know we have to be able to do it, but we would rather avoid, so we can easily impress ourselves with a nice job. If you can land adequately with power off, you're safe, keep that skill current, and then sneak in a little power when you want to impress your non pilot passengers with a good landing.
For the OP, following your instructor's advice, and concentrating on a properly flown approach would be your best bet. You can learn to be lazy later!