I've seen the analogy that "voltage is the dam and the current is the flow rate". I understand the analogy, but I really don't understand why it would work that way. If I have 1500 w of continuous power available, how can in matter if it's built up by voltage or current? The first thing that strikes me when listening to a class D amp is how fast and dynamic it is, surely because of all the available power. Maybe I don't get it 100%, but I do trust my ears.
Also remember that class D is widely used in subwoofers and PA systems, and both applications need lots of power. One last thing to remember, also mentioned in this thread, is that the efficiency of class D amps are around 90% which means that less current is wasted into heat and thus lesser need for beefy power supplies (a good power supply is of course never bad though).