My child refuses to practice between coaching sessions. Does it matter?

Public speaking is a physical skill, closer to a sport or an instrument than to a school subject. Skills like that improve with reps. A student who speaks only in their weekly session is still improving, just more slowly than one who gets a few extra reps in between.

The resistance is almost always to the word "practice." It sounds like homework, and a student who is self-conscious about speaking has little reason to volunteer for more of it. So drop the word and build reps into things that already happen:

• The dinner-table minute. They get sixty seconds to argue for something: best pizza topping, whether homework should exist. You time it. That is a rep.
• The car recap. On the drive, they explain a movie or game to you as if you have never heard of it, with a beginning, middle and end.
• Teach it back. They teach you one thing they learned in their last session. Explaining a skill is practice of the skill.
• One recording a week. A two-minute video on a topic of their choice, sent to their coach or a grandparent.

None of these looks like rehearsing a speech, and all of them are speaking to an audience with structure, which is the actual skill.