Isn't the meter impedance dependent?

If it is a conventional wattmeter, and Mc being old fashion afaic, no. It should be based on voltage and current, not impedance. Please don't get me started again on the misuse of technical terms again. I wish manufacturers start respecting the intelligent of their customers and use the right terms such as "average power", current (in amps/amperes/A), voltage, VA, instead of the popular error "rms power" that has no practical meaning.

I just think the public can understand it, if you explain to them, a moving coil loudspeaker will make sound when the diaphragm moves, and it moves when there the signal current flows, and current flows when the signal voltage is applied, and signal voltage, current are phasors (think vector on the mechanical side) so it has magnitude (unit in A) and phase angle relative to the voltage phasor (unit in degrees). So it isn't that complicated for most to follow, without Googling and might end to reading hearsay, spreading misconceptions like Covid.

For those who wants to understand a little more about the relationship between voltage, current (V, A, Degrees), spl (dB0, then they can Google and hopefully found the basic formula such as Power (VA) = Voltage (V) X I (A), Power (Watt) = Voltage (V) X I (A) X Cosine (Phase angle), and to get 2X SPL, the signal voltage to the speaker needs to go up by a factor of square root 2 (√2).

Yes it is easier to just use the single term Watt, or the incorrect term rms Watt that speaker "needs", but if the right term(s) are used, people would naturally have a better understanding of how to read amplifier specs and better chance to pick one that meets the requirements of their speakers.

Sorry, my frustration is not directed at you at all, but you just asked such an interesting question that triggered it...