while i really cannot commment on sensitivity of Harbeth speakers to variable stand quality, I have noticed with my own speakers (old english budget 2-ways, long out of production, Arcam delta 2 for your reference) an astonishing refinement, when I put them first time on very rigid & heavy, welded DIY stands, made of massive steel profiles, filled with sand and damped with wooden plates glued to metal top and bottom plates, so that they could serve as dead silent anti tank barriers. Spikes of course serve for “decoupling” (I put this under quotes, because it is not what is happening IMHO, instead, I’d call it firm grounding of cabinet on 4 defined points).
In the last weeks before first trial on new DIYed stands I had them positiend on some wooden “stools” of a slightly wobbly static (used to find best hight & tilt angle etc); note the “anti tank barriers” were built to hold the speakers in identical position. At first trail on new stands (and me acquainted to the sound they had on the wobbly “stools”) the speakers surprised me with the removal of boxiness, removal of mid- to upper bass hump (and lard), cleared voices, had deep(er) bass which also tightend up and got more punchy, hard stomps sounded (and still do) more like real stomps on the floor etc etc., and there was a fine 3d sound image which seemingly had little to nothing to do with the speakers. So, all in all, quite a transformation.
Certainly, speakers of doubious cabinets, prone to all sorts of resonances might benefit from rigid stands alot more than e.g. the excellent Harbeths (and where controlled plate resonance might be part of the concept?). Still, I want to offer my experience to inspire others to perhaps trial a possibly real good set of purpose built stands if you get the occasion.
I definitly confirm the importance of hight, but I’d like to add: bass and fundamental tone are also to notably influenced by stand hight, not only treble related aspects.