I'm gonna reply here without looking up any of the relevant caselaw, but I'm fairly certain that the sort of invitation the coach in your hypothetical is making is considered coercive enough to be mandatory. Can you imagine the balls the first/only kid to not go in the corner has to show? We just can't expect/demand that of school children in the face of teacher-led peer pressure.
When I played junior high basketball (and was still a devout Xian & YEC myself), I didn't feel comfortable saying the Lord's Prayer before games with all of my Catholic coaches & teammates, but I sure as hell wasn't going to not say it. I'd've been shunned like nobody's business. That's exactly the sort of situation this is meant to prevent.
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