I do not see the point of either of your examples of rote learning. What do you lose if you do not know the? You will pick up enough of multiplication tables through doing maths, native speakers of a language will conjugate correctly without memorising (you do need to do it if learning foreign languages). Anaphora is a technique which cannot really be rote learned - and most people to try to use it do so badly and just sound repetitive.
reply> You will pick up enough of multiplication tables through doing maths
replyYou will not do maths casually until you have memorized enough multiplication to make it not torture. You will not pick up multiplication from using a calculator any more than you will pick up programming from using a computer.
> native speakers of a language will conjugate correctly without memorising
They do not. They have memorized, through massive, constant, and forced practice, and now they conjugate correctly. The alternative of consulting a computer every time they need to speak is not a realistic one.