@BeefyBill OK, here are a few stats for comparison, between UCSD (a well regarded UC) and Santa Clara (which is really a small private university, rather than a LAC):
Acceptance rate, Fall 2017:
34% UCSD
54% SCU
Composite ACT range, enrolled freshmen:
27-33 UCSD
28-32 SCU
Student-Faculty Ratio:
19:1 UCSD
11:1 SCU
4-year Graduation Rate;
55% UCSD
85% SCU
Average Net Price, per year:
$14,616 UCSD (in-state)
$38,900 SCU
Sure, SCU looks like a nice alternative – until you get to that last pairing. Yes, the SCU kids are probably happier (in general). They also happen to be richer (in general). Realistically, you may or may not be able to afford that kind of happiness. Same reason why you might choose to fly in Coach, even though most people in First Class are probably happier and more comfortable.
Some private colleges and universities are very wealthy, and offer fantastic financial aid (think Stanford, rather than SCU). In such cases, the net price may be competitive with a UC or CSU. But the catch there is that such schools are typically flooded by highly-qualified applicants, so it can be very difficult to get in.
If your daughter is attracted to elite private LACs and small universities, then she could certainly apply to some. Note that there may be more options in the Eastern US than in California. However, you might want to run the Net Price Calculators first, to see if they are realistically affordable, before encouraging her to pursue this option.