I don’t even know that there IS a “general perception” of Caltech. Heck, one of the most popular TV shows in the past decade is more or less explicitly set at Caltech, and my sense is that less than 5% of the show’s audience could identify it.
It’s kind of ridiculous to debate where it stands in a pecking order that is purely hypothetical to begin with and where it has about a tenth the name recognition of the others. If you are talking about a kid in Los Angeles who knows he wants to be an engineer or maybe a physicist, of course Caltech is a first-rank institution. If you are talking about a kid here, even a sophisticated one, who maybe wants to do something in STEM, but maybe economics instead, or medical school . . . Caltech never enters the conversation.
Among my kids’ friends and my friends’ kids, there are dozens who have applied to Stanford (and several attended), at least 7-8 who have applied to Berkeley, and others who have gone to USC, UCLA, Pomona, CMC, Santa Clara, Davis, Redlands. And lots apply to MIT. I am not aware of a single kid who applied to Caltech.