"I think knowing the fact that multiplication is multiple addition, is far more important than being able to parrot tables."
Not necessarily true for children who aren't as good as you at maths. People don't learn tts to parrot them. They learn tts to use in other maths. It means that while you're to work out which fraction turns upside down, or what to add and divide to find a ratio, you're not also thinking about the arithmetic. You can focus on the method.
I think what you suggest is damaging and has held sway over the curriculum for a very long time. It might work if you're lucky or different but for the vast majority good tt's open the door to further applications and more complicated maths.
I hate that phrase "parrot tts". You're a mathematician - you KNOW they have a function, and essential function. Don't pretend.