I think that 7+7+7 is short enough, with enough general arithmetic skills. Probably the best drill for that is keeping a running total at a external pace; that will take a long time to get boring if the total is something you care about.
If 7+7+7 requires paper and 'carry the one' twice, then the problem isn't with multiplication, the problem is with addition. At the very least, everyone should be able to find the difference between two numbers when the difference is four digits or less, in their head, in the time it takes to receive change. People good at math should be able to add small amounts so that the change contains fewer coins.
That particular practical requirement doesn't require being able to multiply 7 by 3.
There's a large gap between 'fast enough to be a decent substitute for a LUT' and 'needs paper'. There's no doubt that one needs to be ABLE to add 7+7+7, but I don't think that each repetition on the path to memorizing 3*7=21 needs to involve it.
Although my 8-year-old son likes his teacher, he is frequently bored at school. He attends a high quality suburban public school in the United States. He has a lot of traits in common with LessWrong readers, and we would like advice for what he can do to counter his boredom. Many of you must have found grade school more or less tedious. What were your coping strategies?