While the idea in its pure form seems ridiculous, she does have a few points that need some consideration.
When a sport becomes too concentrated with only one ethnic group, it does reduce the overall interest in the players and the sport. with professional sports, it can reduce attendance at the games.
A few instances: Tennis - aside from the Williams girls, the USA has not produced any top notch players in at least a decade. American interest is down which further lowers the number of young people training in a sport.
Another example - the NBA is mostly black kids from the inner cities, and since they are great players, it is fun to watch them - until it gets boring as they all seem to become a blur as they play so fast and are mostly hot dogging it - interest wans among many fans.
I think Phyllis Schlafly is incorrect in banning foreign players - but her observation does have some legitimacy.
The majority of MLB players are white Americans.