> You will pick up enough of multiplication tables through doing maths

You 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.