Dufo,
All aircraft will require more power to fly at slow airpeeds such as on approach vs higher airspeeds such as LRC or max endurance, this is due to the effects of the two primary types of drag an aircraft has to overcome; Induced drag, which is greatest at higher AOA's and low airpeeds and gets less the faster you go, and Parasite drag which is proportional to airspeed and gets greater the faster you go. The aircraft has to overcome the combined effect of these and hence if you were to draw a graph of TAS vs total drag you would get a U shaped curve. From this it is possible to see that an aircraft can actually be flown at two different airspeeds with the same power setting, albeit the lower of the two speeds is substantially less than the minimum speeds typically used on approach. This is one of the reasons that primary students are taught slow flight.
The other reason an aircraft will use more power on approach is simply to overcome the drag of the landing gear and lift enhacing devices such as slats and flaps, and lets not forget in the case of the concorde that drooped nose has to add quite a bit of a drag.
And before anyone jumps on board and says "See, you just said it, you can go faster with less power!" just remember, the minimum power required occurs at L/D max for any aircraft which is typically around the airspeeds required for max rate of climb (since max ROC occurs at a speed where there is the greatest excess of thrust) as you go any faster than this speed (typical cruise speeds are substantially faster) you will require more power, period.
Diving down to an altitude may get you a higher TAS initially but sooner or later the laws of physics will prevail and you will get the same airspeed. In fact, if you think about it, the diving down method will be less efficient since you will have climbed higher than necessary and wasted fuel in the process.