The problem with adding a public school isn't that the WCC presidents simply have contempt for them (which is, quite frankly, pretty ridiculous), but that they have much different sources of funding and can have very differing philosophies about education.
A big public school that has football must, by law (Title IX), match the money they spend on football with what they spend on other sports. That can lead to big discrepencies in budgets. Not only that, but public schools have a steady stream of tax dollars (dwindling these days, but still), while privates necessarily are reliant on tuition on donations.
Additionally, the education side of things matters. Never forget that it's the school presidents that make these decisions, not the athletics directors. The presidents are all academics, and generally come from the faculty side of things. And aligning yourself with like-minded institutions that have similar standards of academics is a key part of determining conference expansion, even in conferences like the Pac-12 and Big 10 (which is, without a doubt, the snobbiest of any conference outside of the Ivy and Patriot leagues when it comes to academics).
It makes sense to be in a conference with schools that have generally equal access to resources and have similar academic requirements - that at least ensures a somewhat level playing field.