There were, but it was considered culturally shameful to the family cheat in the same way, which meant that theres an ongoing effort to jack up exam difficulty by making it esoterica which of course only the favored scholars could have learned and blind fire wasn't going to get.I mean, there were constant problems with people cheating on, or bribing the proctors for, the Imperial Exams in China too. The Chinese didn't just somehow robotically follow a social pattern that Romans would have instantly broken; there was a real back-and-forth between those who had the incentive to break it in their favor, and those who kept enforcing it (when it suited them) to preserve their control over institutions.
Given the role the Imperial Examinations actually played in China, I wouldn't rule out being able to institute something similar in Rome- but you'd have to do it after the Imperial period had begun, because in the Republic there isn't any civil service for the test to act as an entryway into.
But Rome in this era was a very personal endeavor. Not using every tool you have at hand would just leave you noble, but never approaching power. Everyone wanted to be the very best. But there can only be one.