Having a real difficult time understanding the OP’s question, or point here:
Now my assumption is that damper to which coills are ,say, pressed
by tension wire balance cantilever/stylu combo in ''all directions'';
left and right and above and below . BUT they also MUST FOLLOW
the GROOVES.
This description applies to many MC carts, and many Audio Technica carts. Not so much to a great many MM carts.
“Damper to which coils are pressed” ONLY applies to MC carts, a very narrow application.
So, are we talking about weakening of the damper? Elongation of the tension wire?
Every cantilever must have a spring force, and a damper. Some styli use a spring and damper in the same suspension (elastomer block). AT uses a tension wire spring and a donut damper ring. Shure used a spring tension wire, and an elastomer block for damping and high frequency spring; Stanton used a variation of this, as did Empire.
Loss of damping over time can occur, and depends on the elastomer compound. In all cases, there has to be a force (spring) to return the cantilever to its neutral position after every excursion forced by groove modulations. A loose damper will hamper this.
I have 163 cartridges, most I have repaired or rebuilt the stylus assemblies myself.