From Stanford's point-of-view, I think KLS is being viewed as the "IT" player who will lead them back to national prominence starting with the 2015-16 season, after what is being considered a "down year" next season.
If you look at Stanford's team next season, none of them were Top 10 coming out of HS (the highest ranked being Erica McCall at #11), the first time ever this has happened at Stanford since the late 80s. Even during their down years from 1999-2004 when Stanford never went past the Sweet 16, they had Top 5-10 players like Carolyn Moos, Lindsey Yamasaki, Jamie Carey, and Nicole Powell.
KLS at #2 is an uber elite player compared to her older siblings (Bonnie was ranked #60 while Karlie was ranked #72 by Hoopgurlz), and will be asked to carry Stanford back to the top. So, as far as playing time is concerned, she will definitely be given lots of it at Stanford from Day 1 , more than she will have as a freshman at UConn.