Are tongue twisters useful for teaching a language?

I am an English speaker raising a son in Japan. He's beginning to study English seriously at school, so I think my best role is to try and teach him less seriously. Today I invented the following phrase for him:

I rarely say "really" when I really mean rarely

He took it in good humour and rolled those r's around in his mouth for a while. I'm kind of proud of my invention. He swallowed it happily.

Generally speaking though, are tongue twisters useful for teaching a language?

My main effort, and pleasure, for teaching my son English is to take turns reading a book in bed, and yakking about the plot and events in the story.

Bite-sized pieces of novelty are surely not as effective as the meal of an entire novel.