donjr, that's correct; and I would say at least 95% of cabinet sidewalls flex.
Cabinet flex was/is more of a concern with old monkey coffins. Its pretty much non existent in todays narrower speakers with more emphasis placed on cabinet designs, thicker baffle and walls constructed from superior material, and internal bracing.
Eliminating resonance by minimizing cabinet flex will improve sound, more or less. But I think your approach is all wrong. I go about it on the inside with hardwood dowel. Or by thickening wall density by laminating similar material to existing. Or some of both.