Not so much worn plastic, but there is a rubber tire sandwiched between two plastic (I suspect nylon) discs. This tire gets compressed between the two discs when movement of the tone arm is called for. Essentially, it acts as the friction component jn a clutch. At nearly 40 years old now, the tire is hardened and slicked off causing it not to grab the upper plastic disc, this in turn preventing rotation of the mechanism, or at least in part.
At issue is how to replace the tire. It is attached by some means to the lower plastic disc, and presumably is glued. No idea what type of adhesive was used as it is difficult to get permanent adhesion to nylon, especially with a dissimilar material like rubber. Removing the existing tire entails the risk of damaging the plastic disc with no assurance a new tire can be successfully atached.
Aside from the above issue, there appear to be other problems concurrent with the perished rubber tire. This is a very mechanicalIy complex setup that Is also heavily reliant on electronics and precise timing established by optical and mechanical sensors. If all isn't working in concert as designed, nothing happens and a time-out error occurs which locks up the turntable until it is powered off, repeating the CPU.
Since it always times out - presumably due to lack of expected sensor feedback caused by a failure of mechanism movement - it matters not how many attempts are made, the tone arm will never move and will lock out every time.
In a nutshell, it's too complicated for it's own good, making it tempermental with age. A solid example of over-engineering to gain a performance advantage with the tradeoff being loss of long term reliability.