Follow up email with better example to interview question?

Hi, I had an interview yesterday but felt I could have done better with at least one of my responses. I've read that some people in similar situations have followed up with an email thanking the interviewers and including something along the lines of "I've been thinking more about your question about X \[insert better example here\]". I feel like this could be valuable but also that it could look like I'm overthinking or wasn't prepared enough. Interested to hear people's thoughts on this (and yes, i know I definitely am overthinking it 😅)