Disagreed, exercise of all kind is known to help with neuroplasticity, complex movements such as dancing and compound lifts even more so. I can easily see how being unable to do any of those things could at least contribute to mental decline.
As I understand the medical science, it all comes down to stimulating the brain and there is no harder stimulation than physical feedback. Lack of mobility means lack of the biggest source of brain stimulation, which leads to accelerated degeneration.
movement/neuroplasticity/physical stimulation absolutely helps - hence PT, exercise classes, etc have being an important part of treatment
My point is, though - the onset of decline in gait ability typical of Parkinson's patients, is a sign of a decline of cognitive ability because the ability to perform gait and all the inherent brain commands associated with gait, is very much a cognitive function as much as it is motor.
One can argue that good DBS therapy by helping keep patients active and engaged does, at least indirectly, help cognition in that sense. BUT - it is consider not to directly treat Parkinson's dementia if a patient is unfortunate enough to come down with that aspect of disease. i.e. it's not like we can switch the device on or fiddle around w/ the programming and the patient's cognition directly improves from the brain stimulation itself.