The reason your 8 watt per channel ASL amplifier is capable of driving the AKG K1000 phones to full output, while other low to medium powered amplifiers are less capable, is related to the ASL amplifier being tube based and not solid state. Tube amplifiers tend to excel at being able to provide the larger peak to peak voltages needed to deliver this level of power (3~10 watts) into a high impedance load (120 ohms). Tube amplifiers run out of current delivery capability long before they run out of voltage capability. For solid state amplifiers optimized for 4 or 8 ohm speaker loads, just the opposite is often true.
From Ohm's law: V = I * R (where V is voltage, I is current in amperes, and R is resistance in ohms), P (Power in watts) = V * I
Power can also be expressed as P = (V^2)/R ( The voltage squared divided by the resistance.)
Example: 1 watt = 2.83 volts ^2 / 8 ohms
For an impedance of 120 ohms, for 1 watt, the voltage needed is:
V = SQUARE ROOT(1 * 120), and V = 10.95 volts
For 3 watts, V = SQRT (3 *120), V = 18.97 volts
For 10 watts, V = SQRT (10 * 120), V = 34.64 volts
A solid state amplifier designed for speaker loads of 4 or 8 ohms that can provide a peak to peak voltage swing of 10.95 volts is capable of:
P = 10.95 volts ^2 / 8 ohms, P = 14.98 watts (15 watts @ 8 ohms).
A solid state amplifier that can provide a peak to peak voltage swing of 18.97 volts is capable of:
P = 18.97 volts ^2 / 8 ohms, P = 44.98 watts (45 watts @ 8 ohms).
A solid state amplifier that can provide a peak to peak voltage swing of 34.64 volts is capable of:
P = 34.64 volts ^2 / 8 ohms, P = 149.99 watts (150 watts @ 8 ohms).
A solid state amplifier rated at 100 watts @ 8 ohms needs to be able to provide a voltage swing of 28.28 volts. At 120 ohms this is the equivalent of being able to deliver 6.66 watts. So an amplifier rated at 100 watts for use with speakers can drive the AKG K1000 phones with a decent amount of power, but one rated less than about 45 watts may not be capable of delivering enough power at the higher 120 ohm impedance.
The 12 watt per channel amplifier that started this discussion is only rated for that amount of power at 4 or 8 ohms. At the 120 ohm impedance of the AKG K1000 phones, the available power will likely be less than 1 watt.
V = SQRT(12 watt * 8 ohms), V= 9.79 volts.
At 120 ohms, P = 9.79 ^ 2 / 120, P = 0.79 watt.
Even if the available peak to peak voltage was a bit higher, say 10.95 volts, the available power would still be just 1 watt.