This goes to the heart of the problem when one equates power with volume. Power into a load varies with the impedance of the load. Since a speaker has a variable impedance with respect to frequency the power delivered also varies with frequency.
More to the point, the output of a driver is directly proportional to the excursion of the cone, and excursion is directly proportional to voltage applied, not power.
For this reason the entire concept of quantifying SPL at 1 meter/1 watt is intrinsically flawed, as SPL is never measured with a constant power input, always with a constant voltage input. By the same token rating amplifier output using power as the standard is intrinsically flawed, since it's voltage swing that determines how loud a speaker may be driven. The situation isn't at all dissimilar to light bulbs, where the assumption was long made by the consumer that wattage, not lumens, was equivalent to brightness.