Systems usually don’t wear out just a part, it is usually a collection of components that work in concert that wear out over time, so freshening up the complimentary items (when feasible) is always wise.

If it helps, consider the children’s song “The hip bone’s connected to the leg bone, the leg bone’s connected to the knee bone…” stress and strain on one part is rarely isolated, and if you only replace the broken widget, the parts the widget interacts with (or counteracts) is usually worn as well and will now reach a failure point sooner as the new part will be resilient and often passes strain on to the surrounding components.