This is the key point. It doesn’t mean that she should choose UW over William and Mary. She may want to learn a lot of stuff that she couldn’t fit in with the requirements of a UW CS degree. But this is a very personal choice for your daughter, and I think that there are pros and cons for each approach.
My own D1 studied computer science, taking roughly the minimum and spent a lot of her time studying her other interests to get the well rounded education that she wanted. She got a great CS job for 2 years after graduation and is now in a excellent PhD program.