Arithmetic strategies are great but you still need a bunch of quick operations (like doubling and multiplying by 10) and fundamental lookup tables (like basic multiplication tables, squares, powers of two) to bootstrap them from.

I don’t think knowing all the times tables up to 12 is as helpful as having a good appreciation for how to break a multiplication into simpler parts, but you do need immediate recall on multiples of all the single digit numbers, up to at least times five or six.