As I understand, it's not really the issue of rote learning particularly, but that exams have a set syllabus, so every child in the country doing the exam is expected to know the same stuff. Obviously in arts/ humanities subjects, there will be a bit of flexibility (or can be, if the questions are framed to demonstrate principles etc rather than eg knowledge of an actual text or a period of history - that can be answered with reference to the text or period you DO know about) but in sciences/ maths, you need to know a certain amount of facts/ methods, or you can't be said to have an understanding of chemistry, or geometry or whatever. So pupils get crammed with this knowledge in a "rote" way in a short period of time, rather than learning by experience, or following areas that interest them.
Continuous assessment (if done properly) may be better at addressing the depth of knowledge in a particular area, rather than breadth over the whole syllabus on a set date. (By continuous assessment I'm talking more about coursework style stuff, rather than just "smaller" exams/ class tests taken more frequently). But ultimately, exams favour the kind of people who are good at exams, good at remembering facts under pressure and so on (and in most circumstances knowing that it is the candidate's work you are assessing!) whereas coursework assesses someone's actual ability to understand, assess and present their topic with access to whatever resources they need and without time pressure. So better at assessing ability to apply knowledge in the real world (imo), which is kind of what CFE was aiming for.
Obviously there are different kind of exams (practical, open book, oral etc) each with their own benefits and drawbacks. But if they are centrally set, candidates will be expected to draw from the same pool of knowledge, and if they are locally set, there is the issue of moderation of question challenge and marking between schools, which can't be an easy task.