Even if damping is removed they might not be reversible. Logic gates that were found to be individually reversible, were found to have difficulties operating when connected in a circuit:
https://core.ac.uk/download/pdf/603242297.pdf
This is very interesting because according to one of the authors of the mechanical computing paper(personal communication) they never dynamically simulated the mechanisms. It was purely kinematic. So this web browser simulation is new work. Reversibility might disappear once dynamics are modelled.