If she’s really that good, the chance of her getting rejected by 17 schools is probably small, independence not withstanding. Nonetheless, every year there are students with no place to go, and every year, there are surprisingly good colleges who came up short who are looking for more applicants. If getting rejected by 17 schools doesn’t tell you to lower your sights, then I’m not sure what will. Also, if you’ve written 17 applications, it shouldn’t be hard to recycle an essay to apply to more.
A forced gap year is rarely absolutely necessary.