How will I know if this person is good at, say, sales or biz dev in a vertical with long lead times? I can't vet that skill set directly; I can only ask the candidate about it. Behavioral questions give me something to cross-reference in the absence of on-the-spot performance data. So do case questions, which (at least ostensibly) tell me how a candidate thinks, and how she organizes her thoughts. (And of course, domain-knowledge questions help me assess the depth and quality of a candidate's experience in the field.)
Behaviorals aren't perfect, though. They can be gamed. It's not too much of a stretch for a candidate to memorize a half-dozen anecdotes to trot out in response to any question that begins with "Tell me about a time when..." (Nevertheless, you'd be surprised by how few people do that sort of prep work.) Canned responses are especially common with candidates straight out of school or grad school, where they are often trained in how to answer behavioral and case questions.
These types of questions probably cause me more stress than any other. Being asked to think of a situation where you felt a certain emotion or had a certain mental experience is not actually that easy for everyone. My memory is terrible at that kind of thing.
It's like my memory lacks a necessary index for what you are asking. I can start going through every major work experience I've had in sequence and filter out the ones that fit, but we might be sitting there in silence for 2-3 minutes which gets awkward enough in itself.
And it's not an inability to remember mistakes specifically, I mean the old "tell me about a time where you solved a problem with no prior knowledge of the domain..." gets me. I solve problems like this ALL THE TIME. That's a skill I have. Fetching those times from memory is not a skill I have.
Luckily I've had these questions in enough interviews that I generally try to have some examples in mind.