As my background is in East Asian political science/history, I’ll focus my analysis on the historical and modern East Asian civil service system and compare it to the current American model.

While not to the extent of Imperial Chinese or Korean civil service exams, the US does in fact have mandatory civil service exams for certain federal jobs, such as the Foreign Service, CIA, FBI, Secret Service, IRS, and others.

The biggest difference stems from the fact that the imperial Chinese examination system was meant to assign most (leadership) governmental positions based on a single unified series of tests. The American system has differing tests for specialized branches and areas of work.

There are two reasons for this difference. First, the Chinese simply didn’t have the resources for specialized national exams for each government position a thousand years ago. This sort of organizational “technology” and understanding just wouldn’t have been feasible back then. More importantly though, is the philosophical and political underpinnings of the Chinese exam. The tests were focused on Confucian philosophy under the idea that good leaders must be good Confucians - a theory which, while ultimately (seriously) flawed, held water back then as a good part of Confucianism was about how to govern people. This approach was criticized by the merchant classes throughout history, and is linked by some (especially Korean) historians as one of the causes of institutional rot that prevented modernization and encouraged reactionary ideals, but I’m getting off topic.

Having explained the differences of the generalized historical imperial system, let’s compare the difference between the American specialized separate series of exams and the modern version of the Confucian-based consolidated/unified civil exam system that East Asia uses today. I’ll compare Korea’s current civil service system, which uses the above East Asian method and is a direct descendant of the Korean/imperial Chinese examination system.

In Korea today, we use a unified civil service system which, like it’s historical counterpart, is notoriously difficult (though not as bad as it used to be). Unlike in the past which tested for Confucian philosophy, these tests examine your logical thinking, data analysis, situational judgment and such, very roughly like a harder SAT that tests for white collar positions. You start by taking the lowest rank test (rank 9, I believe), in which passing guarantees you a certain level of government work. I believe rank 9 guarantees work similar to the DMV and other clerical work, but the Korean government pays a stable wage and good benefits, making these jobs relatively competitive. You are then promoted either via seniority or by passing higher level tests, which opens you up to more and more leadership oriented or complex white collar work. Specialized fields such as foreign service and the Korean CIA require separate, specialized tests like in the US.

In summary, while there are significant differences in the historical imperial system to the American one, most of these are rooted in historical limitations and dogmatic adhesion to Confucianism. More interestingly, the differences between the modern East Asian system and American system touches on the fundamental difference in government operation. The Korean civil service system is premised on the idea that even basic governmental jobs are relatively competitive to their private market equivalents. These job, while they typically pay a lower base rate, provide numerous government benefits and a nice retirement package. While there are definitely overall economic arguments to be made regarding the strength of Korean private markets which influence this, this idea of a government job as holding some base prestige is a historical line of thought created from the imperial civil service exams and is maintained in an altered form today. The idea that American government workers such as DMV workers should be a competitive position that provides a stable retirement fund is an idea that runs counter to both American cultural understanding of the private market and its conception of individualism.

What a nice answer by /u/kingkahngalang. Let me add a bit on the United States side of things.

The main reason why the Civil Service Exam in the United States was both limited and largely useless was it came out of the reform of patronage - which most in politics at the time didn't really want.

Patronage had pretty much been around as long as the Constitution; if you go back to the Election of 1800, one probable reason why Jefferson defeated Burr was that part of the deal he offered James Bayard was probably to let him select several Port Collector positions, which were rather lucrative. But if you fast forward to the 1860s, Grant's administration is one of the most corrupt in history, and one significant aspect of this was in who he chose (and accepted) for patronage appointments.

As Grant leaves office under a cloud and the Republicans become less and less concerned with Reconstruction, the most prominent split of the party is not on ideology but on the degree of graft. The stalwarts are the portion of the party that believes patronage was the natural order of things and that political machines were effective administrators even with incompetent office holders; the half-breeds are those who object to that. Even the half breeds are somewhat lukewarm about complete reform, though; both political parties got about 10% kickbacks in salaries from their office holders and appointees, which was the major source of campaign funding for the 19th century.

So this struggle continues for the next few years with varying cries for reform, right up until James Garfield is assassinated by a crazed office seeker who thinks he's entitled to be appointed Ambassador to France. This pushes the argument over patronage to the forefront, and finally forces Congress to act with the Pendleton Civil Service Act.

But that act is deliberately watered down from the beginning, and even worse, doesn't result in even some of the least optimistic plans of it. I'll quote Richard White's comments from Oxford's The Republic For Which It Stands since they're such a succinct, damning conclusion:

"The results were not what reformers intended. Rarely has a law so failed to achieve its stated objectives while creating a set of unanticipated consequences. The Pendleton Act initially affected only a relatively few “classified” federal appointments—about 10 percent—which were merit-based and required successful passage of an exam. It, however, did expand relatively quickly. Within five years of passage, half of federal appointments outside the Post Office fell within the scope of the act, although not until the twentieth century would 80 percent of federal appointees achieve civil service status. The act had a loophole that allowed bureau and division chiefs to hire whomever they wanted for positions above the test-passing line. The act thus transferred political power as well as social power to those chiefs. Nor did patronage vanish; it took up residence in new places...

"..and instead it created a nonpartisan gloss on a persistent partisan system. Presidents continued to replace members of the opposing party with members of their own; they just did it differently. After the passage of the Pendleton Act, removal from office did not appreciably decline in periods of party turnover; indeed it sometimes increased. Before the Pendleton Act new presidents had dismissed officials from office as soon as their own terms began; after the passage of the act they did not resort to early terminations. Instead they waited until officials’ terms expired and then replaced them. Since most terms ran for four years, commencing with the beginning of a new administration, the net result was that officials served a few months longer than they would have without the act. Presidents could, however, use the act to protect holders of new offices, whom they appointed late in their administration. Their successors would be stuck with them until the appointee’s term of office expired."

So that was why no serious attempt at a much deeper civil service exam ever took place; the parties didn't want to change patronage any more than they already were forced to.