Ryder - power supply capacitors are recharged in very short current spikes of high amplitude. High frequency of these spikes heats-up the core of transformer while rms value heats up the copper (windings). This rms value, because of shape, is much higher than average value delivered. As a result transformer with rectifier/capacitor load needs much higher rating (at least 50% more) than transformer with resistive load.
That is important when you need large constant current (class A) while typical class AB amps have much lower requirements since average music power is only few percent of peak power and peak power is handled by power supply capacitors (unless you listen to sinewaves at full power).
Power supply capacitors are in series with the load (circuit closes thru them) and not only capacitance but also quality (ESR, inductance etc.) is important. For instance, if they used high inductance capacitors adding film capacitors will help with response but will create parallel resonance circuit that rings.
So, transformer is important but I would also pay a lot of attention to power supply caps since good ones (and a lot of them) are expensive (like slit foil caps).