This!
It sounds like your parents are willing to pay somewhat more for prestige (i.e. UCLA)… but there’s a big differential between the in-state cost of UCLA, and full-pay at Yale et. al. If the full cost of UCLA is a hard limit, then the answer to
is yes, you should not bother applying to schools that have no chance of affordability. Most elite privates cost double what UCLA would cost you, or even more. Even an informal debt of >150K for undergrad would be very unwise, especially for a student with career goals that may not be immediately lucrative. You don’t want to end up with a choice between struggling financially and damaging your relationship with your parents, over the money they loaned you.
Look for options that are both good and affordable. In addition to in-state schools in CA, look at schools with WUE reciprocity also. And others that give big merit awards.