I see. Where I learned to fly, the field elevation was five thousand, and the density altitude in the summer was closer to 9,000' to 10,000', for the takeoff. Local terrain was above 12,000'. I think it was ten years before I ever flew close to sea level.
Vx and Vy are functions of power; in the light normally-aspirated airplane, power decreases with altitude, and the values of Vx and Vy change, as well.
I suspect that the original poster may be thinking of published sea level values of Vx and Vy, and asking why these aren't used at altitude. By the time one reaches 7,000', the values for Vx and Vy are coming closer together.
Cooling is one reason, as IO540 noted, though with cooler temperatures, cooling isn't as critical at 7,000 as it may be at sea level on a warm day. Cooling isn't as effective, however, because of reduced flow and a higher angle of attack with reduced power, lower air density, etc. For that matter, it's often advantageous to climb most light airplanes at speeds well above Vy; during a hot day in Las Vegas (USA), for example, 100 is the minimum speed one should climb, for engine cooling. The original poster is from UAE, apparently, and will see similiar temperatures in UAE during the hot season.
If climbing to altitude quickly is the mission of the flight, then Vy as far as one can take it is the answer; getting the maximum altitude available in the minimum amount of time. If, however, getting from A to B is the primary mission, then the best forward speed one can get is the order of the day. One doesn't necessarily need to climb as fast as one can, because climbing isn't the primary goal; getting there as quickly as possible is usually the goal. Otherwise, you might walk.
If you're in cruise at 6,000 and wish to climb to 7,000, you're be much better off with a cruise climb. You want to keep as much speed as you can, and climb at a minimum value to get to the next altitude. Generally five hundred to a thousand feet per minute is the desired rate. You're not going to get that in a light airplane like the 172, so get a climb going, whatever you can manage, and accept a slight speed loss in the process.
If you're cruising at a reduced power setting (not always reasonable in light airplanes), then you can keep your cruise speed and simply increase power, because the technical climb function is excess power beyond that necessary for level flight at a given angle of attack (airspeed, in this case).
If you're using full power in cruise, which is often the case in light normally-aspirated airplanes, then you're probably going to need to find a compromise between best forward speed, and a reasonable rate of climb, taking care not to slow down too much.