Hello,
For a variety of reasons, it is more fuel efficient to accelerate to ECON speed as soon as practicable but one of the most logical reasoning is the engine performance is much better at lower altitude than at higher altitude. Therefore, the aircraft accelerates easier at lower altitude.
The other reason is air is much thinner at higher altitude (by 10000 ft, the atmosphere has 50% less pressure than at sea level), thus TAS becomes much higher at higher altitude. It will take you much more distance to accelerate the aircraft to your final climb speed than at lower altitude, so less efficiency.
A point to note, flying cost index zero is usually not flying the minimum cost. Operating cost is divided into two parts, fuel cost and time cost. Flying cost index zero just means fuel cost is so expensive, u need to conserve every single bit of it. If your company time cost is high, it stands to reason to fly faster so that time cost can be minimized. By burning extra fuel, you can save company money by saving engine and airframe maintenance cost, crew per hour flight cost etc... Cost index zero will mean flying maximum range (MRC). LRC is a speed that gives you 99% of MRC.
All this however, is not exhaustive...