It's funny how maths get held to different standards to music and sport and dance.
When it comes to music and sport and dance, everyone accepts that drilling the basics to the point of automaticity is important, not because the teacher is trying to turn the student into a robot but because being fluent and automatic in the basics (=not needing to consciously think about how to do them) is, paradoxically, vital if you want to get good at the interesting bits. You can't become a sensitive and imaginative dancer unless your limbs and body slide automatically into place; if you have to hover there awkwardly remembering consciously how to do this move or that move, you won't have any headspace left over for interpreting the dance in a creative way. Same with music. It's why music teachers make you do scales and arpeggios and other things until your fingers fall into place without your needing to think about them.
With maths, on the other hand, people seem to think that a teenager who has to sit there humming and hawing and doing dumb tricks on their fingers to work out 7 x 8 is somehow going to be in a better position to solve complicated problems in algebra and geometry later on.
A few people are able to get by in advanced maths without getting their maths facts fluent and quick, because these are the people whose working memories are larger than average, meaning that they have enough leeway to think about 7 x 8 AND the complex bits of the problem at the same time. Most people are not like this, and if they have not got their maths facts fluent and automatic in primary school, then trying to do the hard stuff later on is going to feel like wading through mud. When we are designing school systems, we have to look at what works for the greatest number of people.