1. Covering the times tables in school is pointless when you already know the times tables because you learned them at home.
2. Therefore, people shouldn't learn the times tables?
Saying something shouldn't be taught is a completely different idea from saying that schools shouldn't teach it because incoming students are expected to have learned it already.
But I think there is a grain of truth to it.
Emile, or On Education (by Rousseau) proposes an idealistic goal in which a boy is educated by a tutor (a class size of) without being 'denatured' (losing the innocence and good moral quantities that the romantics think small children naturally possess). I'm not sure how realistic this is - Rousseau had five children but he dumped them all in orphanages as soon as they were born, but I think it rings partly true as something that works if you have sufficient inputs. If you have one really good tutor / parent you can raise a child to really understand things without cold but efficient methods like drills.
Imagine you want to teach times tables without using times tables. You can keep track of what the child knows, and work out fun activities that lets them figure these out themselves, and guide them when they have a misunderstanding. But it's going to be labor intensive (for both the child and the tutor) and can't scale. Maybe computer teaching systems will turn drill work into a more fun system for teaching these fundamentals, since it can personalise at scale, but I suspect the opponents of drill will the complain about how soulless machines are pumping lifeless low-level skills into the heads of children who should instead be learning more high-level things in a more humane way. After all they didn't need a computer to teach them how to read, they just picked it up after their parents read with them every night for half a decade.