(I haven't hit clinicals yet, so please don't take this as gospel. just my take on it) The pro's you listed are spot on, but some people don't like the cons:
1. Only relatively recently have we started to see treatments that can actually yield benefit to patients involved in neurology. Only in the last 12-13 years have we developed any good treatments for stroke, for example. Before it was kind of diagnose and watch.
2. A couple of the common diseases are terminal and involve protracted, horrible declines in quality of life. Take for instance MS, Parkinson's, Huntingtons, and Alzheimers. We can do some things for these diseases now, but they pretty much all involve huge declines in function until complete dependence on other's for the most basic of functions.
3. Pay in comparison to other specialties.
4. The stereotype of them being armchair philosopher's and not "do'ers" (not as true anymore.)