Many teachers regard the responsibility of learning the times tables as something the student simply has to do, normally in their own time e.g. as a homework assignment. Then the teacher will use teaching time to test their students; to make sure they've completed their assignment. This is not teaching, but testing; and it is often embarrassing or even humiliating for students who have difficulty memorizing those lists of times tables answers.
A far better approach, more in line with the expected role of a teacher, would be to actually teach students mental multiplication skill, which they could of course practice as a homework assignment. In the process of helping students develop such skills, the teacher would test as part of coaching that skill. This approach is far less threatening to students.
One of the problems with most method-based approaches to the times tables is that each method (e.g. the 'fingers' method for the nines) is that each individual method solves part of the overall table of multiplication problems, but that the rest of the table needs to be covered by other individual methods. A fully comprehensive approach, however, addresses the times tables entirely, without leaving any gaps.