I think times tables should be taught, but what I really really hate is any teacher who says "Show me how you solve....."
Then tells some pupils they did it the right way, and others did it the wrong way, even if they all got the correct answer. (Admittedly occasionally someones method might work for one problem but not for another, in that case they should be shown that, by trying to solve the second problem.)
I think knowing the fact that multiplication is multiple addition, is far more important than being able to parrot tables. If you can do the second only, you can be overcome by nerves, forget one fact, and be lost.
But then I hate homework at primary, as I found when DCs school still did it; it stopped me doing other things with them. We literally sometimes had to choose between learning spellings or working on other literacy or comprehension skills.