This family has some means, so if they can comfortably afford Stanford (and, in time, whatever school their daughter chooses), fine.
That said, there is a myth out there that Stanford or Harvard offers unparalleled undergraduate educations, and this simply isn’t true. It’s not as if a WF student would be overwhelmed at Stanford, while a Stanford student would find the academics at WF remedial. I’d recommend everyone read Frank Bruni’s book “Where You Go Is Not Who You’ll Be.” Bruni, a writer for the NY Times, turned down admission to Yale to attend UNC-Chapel Hill. One of the biggest myths out there is that there is some huge difference in quality of undergraduate education (undergrad!) between more or less similar universities.
So, yes, the issue is really whether the Stanford name is worth it. Again, we are talking about undergrad here. Undergrad! Stanford’s main reason for existence is not to take families’ 18-year-olds and provide them with four years of rigorous, mentored education and opportunities for personal growth. Stanford exists to create research and scholarship. It also exists to educate and mentor graduate students. Last of all, because there are so many bright minds around Palo Alto, yes, it is willing to “take in” the OP’s son, knowing full well that the Stanford name will have pull. An earlier poster mentioned that WF is buying the OP’s son. That’s true. But it’s also true that Stanford hopes to convince the OP to spend 300K instead of zilch (actually, less than zilch, since the OP’s son would be receiving a handsome stipend at WF).
I am not denying that prestige has value, but as the somewhat well-known Krueger and Dale study shows, for students who are admitted to elite schools but choose to attend a school elsewhere, there is zero difference in earnings over the long run. The student who turns down Penn for Penn State will be just fine, as will the OP’s child if he chooses, potentially, to attend Wake Forest over Stanford. The exception that Krueger and Dale found is for the student who has minority status. People of color, for instance, do benefit from the chance to attend an Ivy or Ivy equivalent.
Normally, the choice here would be a no-brainer: WF. Only the OP can decide if the 300K price tag is worth the name recognition. If the family can afford it (without affecting the daughter’s college choice down the road), great! If not, OP, you have your answer. Oh, and it’s not as if WF is some podunk school that no one has ever heard of.