> In primary school for example, we learn maths by memorising times tables and solving thousands of basic arithmetic problems. This was important in a time before calculators...

I used to think like you on this point, until I taught students who were brought up using calculators instead of memorizing multiplication tables, etc. It turns out that many of them could not figure out how to use calculators when needed--they didn't know what to enter because they were rarely required to do any mental math. It's really important for elementary school students to count out loud (including by 2's, 3's, etc.), and count backwards, and memorize multiplication tables, etc., so they are comfortable and confident doing basic arithmetic. Calculators are for people who already understand how to do arithmetic.