Why is dopamine or a dopamine-receptor agonist not pumped into the brain of Parkinson patients?
Levo-Dopa is used as a first-line treatment of Parkinson's disease. Unlike dopamine, L-Dopa is able to cross the blood-brain barrier. There it is converted into dopamine. To prevent premature breakdown in the gastro-intestinal and circulatory system after oral intake, carbidopa can be co-administered. Also MAO-B inhibitors and COMT inhibitors can be applied to prevent breakdown of L-Dopa in the brain. Oral medication is preferable over invasive intracranial infusion of medication. 


Conversion of L-Dopa into dopamine. Source: ADHD treatments.

Dopamine agonists are also in use. Unlike L-Dopa, dopamine agonists are not converted into dopamine. Instead, they mimic dopamine effects in your brain. They aren't as effective as L-Dopa, but they last longer and may be used alongside L-Dopa to smooth the sometimes off-and-on effect. 

Parkinson's disease is not fatal, but it can reduce longevity. The disease progresses more quickly in older patients, and may lead to severe incapacity within 10 - 20 years. Older patients also tend to have muscle freezing and greater declines in mental function and daily functioning than younger people. L-Dopa treatment in the long run causes adverse effects, such as dyskinesias, toxicity, or loss of efficacy (Marsden, 1994).

Reference
- Marsden, Clin Neuropharmacol (1994); 17: S2:S32-44