The resignation was almost certainly caused by recent revelations about her driving record and the fact that she got the job through political connections without having any real qualifications for it. In that sense, one could conclude that the political process worked well. A compromised and unqualified official was ultimately forced to quit. On the other hand, Burgess held this position for over five years before anyone in state government noticed (or at least cared) that she might not quite be the right person for the job. That may be good enough for government work, but it’s not actually all that good.
UPDATE: It looks like Burgess was already scheduled to leave the highway safety director position. The resignation is from her position as a state employee. Given this situation, it is possible and even likely that the resignation was not the result of the revelations about her driving record, as I suggested above. I apologize for the mistake, (which, however, I caught within 30 minutes of putting up the initial post). It is, however, still the case that Burgess held this position for several years before there was any effort to force her out.