However my intuition is that the rate of climb depends wildly on various things. Aircraft weight, altitude and so on. Furthermore, you could potentially fly at maximum airspeed, and then pitch up 90 degrees, and climb until you begin to stall. Sure you wouldn't be able to last long, but for a short period you'd have a very high rate of climb.
So the question really is, when aircraft specifications detail "rate of climb", is there some implicit context for when that rate of climb is applicable? Is it optimized for climbing in the most time or distance efficient way for X distance or something?