Just bought a HP-67 calculator at an auction

[Chr Yoko]

This "gummy wheels" issue seems to come from the material degradation over time.

Looks like HP has chosen the wrong material and process : Low spec material and/or too cheap process that "forgot" some key steps in order to save on cost.
Typical short cut is avoiding the long post-curring / post-vulcanization step that would link the polymer chains together. Post-Vulc needs to put the parts gently aligned onto a stainless steel tray into an oven for long hours at a specific temperature with a specified ramp-in/out (depends on material compound, part size, geometry ...).

Rubber materials are diverse and some advanced rubbers, if used properly, can survive very severe environmental conditions such as acidic, basic, oils, petroleums, solvants, water , high temps, low temps .... Of course a "one size" fit all does not exist and you need to select the most suitable material for your application and to its cost target since some will cost you well over 100€/kg (FKM-FPM or Silicon for instance).

Look at your engine bay and you will see plenty of long lasting engineered application specific rubber materials ;-)

FYI, i just changed the handlebars grips onto an old MtB because they became overly sticky and we all know about those "ruburized" plastic housings for electronics that also become sticky over time (some computer mouses or keyboards for instance...).
One hypothesis is that those be-material parts can't be post-vulcanized or they would melt the underlaying thermoplastic during the process, so the rubber ends up decaying after a while and under human acidic fluids contact !