In Parkinsons disorder the substanstia nigra pars compacta get affected and there is destruction of the dopaminergic neurons, which ultimately disturbs the direct and indirect pathways. Now we know indirect pathway is overall inhibitory to movement and direct pathway is overall stimulatory. Now because both of these pathways are not working properly, can we consider this as a reason for both hypokinetic and hyperkinetic disorders seen in Parkinsons? Or there is some other explanation.
I am not highly proficient in neuroscience, but I managed to find the following from Sonne et al. (2020) which may help while you wait for a more proficient answer. (Emphasis mine)
While most forms of Parkinson disease are due to the insidious degeneration of the substantia nigra over a lifetime or during old age, the cause of that degeneration is unknown. These forms of Parkinson disease are termed idiopathic due to their unknown cause. A great deal of research is being done to identify these causes, which can include peripheral inflammation, metabolic insufficiency, and various environmental toxins, which have been shown to affect the substantia nigra. Several other neurological conditions exhibit parkinsonian-like signs and symptoms by affecting the dopaminergic neurons of the substantia nigra. These include drug-induced parkinsonism in which a patient is taking a pharmaceutical compound, such as antipsychotics and antihypertensive, that affects dopamine metabolism.
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Sonne J, Reddy V, Beato MR. (2020) Neuroanatomy, Substantia Nigra. In: StatPearls. Treasure Island (FL): StatPearls Publishing. Available from: https://www.ncbi.nlm.nih.gov/books/NBK536995/
The motor system has a LOT of paralell pathways. The model you state is very old and told in med school because it looks nice, but it just doesn't fit the reality. For example, there are a lot of papers trying to come up with models of tremor generation involving corticothalamic loops and beyond.
I suggest reading Motor Control chapters of this book, which is very short and introductory, but beautiful. Neurophysiology: A Conceptual Approach by R. Carpenter, fifht edition. Or you could go with Gazzaniga and even better Kandels'.