What do you mean, exactly, by "replicate the cursus honorum?" If you mean specifically the actual offices that eventually came to enter into what is called the cursus honorum, it must be noted that the Roman system of magistracy arose out of particular circumstances peculiar to Roman society at large. The election of (exclusively) plebeian magistracies like the tribunate (technically outside the cursus in its developed form) or the plebeian aediles would not make sense in a society without a formal patrician order, which could only exist if there was a body of advisory patres existing at the beginning of the tradition from which families could claim descent. Likewise, the existence of offices like the praetorship or the quaestorship would not necessarily make sense in a society that did not develop from a single city-state--the establishment of courts or magisterial financial administration from a single individual does not work in a large polity, and the Romans themselves recognized the need to add to the college of quaestors and praetors. Certain laws, like the laws limiting tenures to a single year, grew out of particular events in Roman history and do not necessarily make sense when moved to other societies. In the case of one-year tenures for magistracy this particular procedure developed, traditionally, from the desire to limit the power of individuals as much as possible. But even in antiquity the difficulty of dealing with crises or getting important business done with only a single year was recognized, and is not necessarily sustainable

If you mean why modern Republics do not replicate the order in which magistracies are held, in a certain sense they do. The cursus honorum only came to exist as a formal structure quite late, following the Second Punic War, during which many individuals had raced through the list of magistracies in record time. In order to prevent this and establish a fairer ground on which magisterial hopefuls could compete legislation was passed establishing minimum ages for various magistracies, which remained the most important form of "regulating" the order in which magistracies were held. Some time in the early second century a law was passed which established that all consuls must be ex-praetors, and in 180 the lex Villia established minimum ages for the curule magistracies. But the so-called "cursus honorum" was not even formally solidified by law until Sulla, who added a minimum age to the quaestorship and set it as a requirement for higher magistracy. Prior to this the only really legal requirement for the order of magistracies had been that the consulship should derive from the praetorship. That had been the grounds on which Sulpicius Rufus challenged Caesar Strabo's illegal consular candidacy in 88. Other than those two regulations, that the consuls should have been praetors and that (more importantly) there were minimum ages attached to the senatorial magistracies, there was nothing until Sulla that actually stipulated that the order of magistracies was required. Instead, the cursus regulated itself, simply because the staggered minimum ages meant that the politically ambitious were encouraged to hold magistracies in the right order, at the earliest age possible. Even Sulla's establishment of the quaestorship as a requirement for higher magistracy only meant that on the way to the consulship the quaestorship and praetorship were now requirements--the aedileship strictly speaking was not actually necessary, and was frequently skipped (there were only four, as opposed to the ten praetors following Sulla). In the same way, most modern Republics have established minimum age requirements for each of the most important offices. In the US Constitution, for example, it is stated that the minimum ages for Representatives, Senators, and the President are 25, 30, and 35 respectively. There's an obvious implied cursus there in much the same way that the original Republican cursus was enforced almost solely by the minimum ages imposed by the lex Villia