Omega_Void
Your Eventual Destroyer
Despite what unrealistic lab-tests you do, the L2 has always been crap for any duties that didn't require utter annihilation of transient content. Regardless of what it does to square waves, it has always had the effect of flattening and distorting source content in, many times, really undesirable ways.
Actually the OP graph shows why L2 sucks.
The tops of the waveforms are flat (just like the input) during the unattennuated part, and flat where the full attenuation has been applied. But in the attack and release the tops aren't flat, they're curved - the waveform has been re-shaped. This means distortion harmonics.
So on musical signals, L2 doesn't distort on the transient peaks, but it distorts immediately before and after the peaks. Hence the obscured, smeary sound.