As I am reading a bit of local Chinese history I am struck by the extent to which the government structure is familiar to that of 1995 (wink wink). For example, the administrative boundaries haven't changed all that much beyond adding a new level with the Township (xiang). More strikingly, the actual administration seems quite similar in its quasi-federalism, as officials are appointed centrally, but they have a high degree of personal initiative within their locale. The similarities between the gaokao and the Imperial examination have also often been noted, albeit somewhat ironically.
So my question is to what extent these are real streams of continuity, if so to what extent it was a conscious decision (on the part of both PRC and ROC) to co-opt the old systems or if it was simply a "don't fix what ain't broke", and whether there was ever a serious attempt to change them.
I'm going to give a somewhat brief answer, confident in the fact that another user will give you more detailed points on the areas I gloss over.
First off, the administrative boundaries have changed quite a bit. Sikang Province is long gone, as are Jehol, Suiyan and Chahar. There's also been quite a bit more shuffling closer to 1995 as well beyond just the addition of the xiang. Then there's the aborted reshuffling of cities and counties subordinate to cities which only really happened in part of the country. Obviously some major borders haven't moved, but these are also often geographical or sociocultural and it wouldn't make sense to move them. There's just no reason. Still, despite this, much has changed.
Second, while the gaokao dates back to the early 50s, it was different in a number of ways from the college entrance exams of Republican China. Even if we were to link it to the earlier Civil Service Exams, the line of transmission is not unbroken. And I don't believe we should be making such comparisons in the first place.
The other and more general point I want to make is that much of what the PRC adopted as their own policies early on, especially in regards to things like education, were often adopted wholesale from Republican China, which itself had made efforts to establish new policies since the mid-teens. Much of these policies weren't officially sanctioned by the PRC until years after the founding of the People's Republic, but then they often didn't need to be since they were already in place as the de facto system. I personally can speak to this in much greater depth as regards to language policy in particular, but it's not limited to just that area.
if it was simply a "don't fix what ain't broke"
So yes, I'd argue that's exactly what it was, but from the Republicans, not from the Qing. The Qing systems were largely replaced in the Republican period, and then the Republican system had the inertia to carry over into the 1950s before either being made official or being modified/replaced.
edit: I can talk more about the history of the entrance exams if you're interested. I kinda kept it short for now.
edit2: I did talk more about it, below. If you're interested.
I'm by no means an expert and I do not have a thorough answer about PRC (I grew up in Taiwan, ROC), but in my undergraduate studies of modern Chinese history (tangential really to my Linguistics degree) and in my studies thereafter, I can point to just a small parts of what happened between then and now that may point to where it has or hasn't changed.
Additionally, someone who has studied this in English, please feel free to correct me on any of the names of ruling bodies because I do most of my reading on this subject in Mandarin and this is difficult to translate:
A conscious decision was made after the Xinhai Revolution by the voting body of KMT officials to both instate a new form of government and also to install Sun, interim president, as president. The old system of the two categories of officials ended there. A new interim constitution based on KMT's very western influence was ratified. Eventually, early election processes failed and Yuan Shikai was elected instead as the second interim president. Source
The installation of Yuan delayed a change in government processes and administration for decades. Firstly, this was complicated because Yuan was a military general who served under Qing dynasty emperors and regents for years and culturally the inertia of old ways was just too difficult to change, because historically military officials have had serious struggles politically with the central government. The interim senate/parliament (am unsure on how to translate this word) saw him as a threat and actively worked to suppress executive powers. Eventually he dissolved the KMT government and their temporary interim constitution, culminating in announcing himself emperor in 1915. It would be years before he would be deposed, and this is in my opinion a good example of the difficulty China culturally had in balancing its executive powers due to holdovers and traditions from dynastic rule. Source
As far as Taiwan goes... due to the Cold War and of course the Korean War, ROC in Taiwan did not gain any real traction as a democratic government until the late 70s. The White Terror was a time of total rule by the KMT and very closely resembled the central-out structure of the Qing Dynasty. Just for a point of reference, I was born in 1987, and at the time there were just 3 government-controlled television channels and private newspapers were just beginning to be printed. In the 70s my mother lived through the Kaohsiung Incident. The government in the ROC was not reformed until the late 80s and the first national presidential election occurred well after I was born, in the 90s. In practice, Taiwan's government and its 5 branches with their checks and balances and processes is very similar on American governmental practices, only with people throwing stuff at each other during lawmaking sessions.
Secondly, there have always been townships or xiang in some form, just not officially administrated everywhere. A quick search of the words 鄉吏 歷史 on Google Books resulted in this reference to a duty of a local township admin during pre-Han eras.
You are correct that gaokao is very similar to the Imperial examination. I am not knowledgeable enough to know the intention of it, but I can confirm that practically speaking, in Taiwan, scoring in the top percentile or percentiles (depending on government work demand) results in the guarantee of a government job which comes with full tenure. It is exceedingly difficult to be fired from a government job, and we still use tie fanwan, "the steel rice bowl," in colloquialism in the same way it was used historically.
On the subject of education and the direct connection between gaokao and government jobs, the current model can also be traced back to Japanese rule. Formal public education in the Western, non-Confucius style was only implemented during Japanese rule and literacy jumped from 3.8 percent to over 70 percent in Taiwan in 1904 to 1943, just before the KMT took over. Japan already had something similar to gaokao at the time as well for their law, medicine, and Eastern medicine governmental positions, and it doubtless influenced the implementation of gaokao as we know it in Taiwan. (Statistic citation and further reading on Japanese rule)