Amazon knows full well what the LP interview experience is like, and it's by design. It's not about "how much you want to work at Amazon", but it's also explicitly, intentionally not about "actually getting to know you".
My friend told me that every Amazon employee has to go through an interviewing training course where they are explicitly told they are not allowed to ask any questions that are not directly related to an LP. In most cases, they don't even get to choose the LP that they are asking about. They are given a specific list of 2-3 LPs, and told that when they come out of the interview room, they must have asked questions about those 3 LPs, taken the answers down as notes, and are explicitly told that they must not ask any other questions or take any other notes.
The explanation I was given is that this is all an intentional attempt to make the interview process as impersonal and consistent across candidates as possible. They intentionally do not want to ask any questions that would lead you to talk about your education or hobbies outside of work, and they intentionally do not want the interviewer coming up with their own, not-pre-approved questions. Apparently they think that this makes it less prone to bias, which I suppose is a good thing in theory, but in my opinion, the execution resulted in a piss-poor experience as a candidate.
Apparently it isn't fun for the interviewers, either. My recruiter warned me that my interviewers would likely be rushed, impersonal, and focused entirely on recording notes about our conversation, because apparently if you are designated as an interviewer you have very strict quotas on the amounts of notes you have to take, and then as soon as the interview is over you have to rush immediately to another interview where you again have to take a certain amount of notes. The entire process sounds awful for everyone involved.