It's a great gesture but in a batch process driven selection like MBBs, it's not necessary and has zero influence on your chances of passing the interview.
I personally would only suggest taking such initiative if you feel your really connected with that interviewer and the feeling was mutual. It really comes across when candidates send a thank you email purely as a formality as opposed to mentioning something meaningful. Either way, at most firms, your interviewer will call you for the turn down or feedback/coaching where they will offer to stay in touch if they want to.
PS: I've just seen that you've genuinely thanked every respondent to your question. It's a lovely touch that doesn't happen too often on this forum where coaches are genuinely offering to help the next generation of consultants. My overarching recommendation would be to be genuine and where for someone like you, a thank you email to each of your interviewers could be very appropriate. I am sure you will also be thoughtful and genuine in the actual content of the email too. Good luck!