I think you might have a misconception here! Its true that the output filter is affected by the load. But it won't change the FR significantly because of two factors. First, the load affects the Q of the filter. What this means is with lower impedances the filter broadens a bit and is less effective- so you might see bit more of the residual (sine wave at the switching frequency). The second is that in a self oscillating amplifier there is so much feedback that phase shift and the audio passband FR are unaffected. Quite literally there's enough feedback to correct for issues that might arise if the filter is operating at a lower Q.Methinks not.
Class D Output filters are load dependent.
From TI:
The LC filter response also varies with speaker load impedance. The load impedance determines the damping ratio of the output LC filter and is classified as overdamped, critically damped, or underdamped. It is also important to understand the speaker load impedance variations for the application and select the L and C values that suit the expected load variations. Ideally, the LC filter value is selected for a critically damped, flat passband, and phase response. Two considerations when selecting components for the second-order low-pass filter is the cutoff frequency and Q factor or damping ratio.
The variations can be small, but they will vary with every load presented. Hence, the perceived sound of the amplifier can vary with each speaker.
This Stereophile image of PS Audio's Stellar M-1200 shows it well damped and relatively immune to load variations. https://www.stereophile.com/images/1220PS1200fig01.jpg
Ditto this Schiit Aegir https://www.stereophile.com/images/919SchAegirfig01.jpg
Not so much this new Mytek Brooklyn AMP+ https://www.stereophile.com/images/421Mytekfig01.jpg
Making a purchasing decision based on the written word is folly. Doubly so for fan-boy recommendations.
I'm not knocking Class D. I have one driving the woofers in my tri-amp system.