Capacitive load is no different to resistive load, the "power" is V-squared-on-Zc. Although for a capacitive load this is apparent power, from an amplifier's point of view it still needs to handle the load. It turns out that a normal push pull amplifier (Class AB) driving a capacitive load is only 30% efficient at best, because the peak current occurs when the capacitor voltage is zero, meaning drive transistors see peak current and peak voltage at the same time (i.e. they get really hot).
So, overall it could take a moderate power high frequency amplifier to do the test, especially for larger transformers.
At 400kHz (IEC 60601-2-2 testing) I solved the problem by adding parallel inductance to create a resonant circuit, that allowed test loads up to 500VA with just 75VA input. I'm not sure if this would be necessary or practical for the x2volts x 2freq test, because each test frequency is different.
There may be a second issue if the core's rated frequency is exceeded. A core that runs well at say 65kHz might saturate at 130kHz, also adding to the load and possibly causing significant heating.
I'm not sure the standard writers really understood the issues well.