But if you used the phrase "That's exactly like", I think it would sound equally forced.

At this point I think it's a matter of empirical testing - meaning, in this case, observing people, since the question is about what people do in the course of normal conversations.

People generally love it if you agree with them - it's impolite because you don't always agree.

This is a significant part of why I said "most possible conversations". I would guess that it's possible to have a political conversation with most people that they'll enjoy - but reliably doing so takes more information than you'll generally have about someone you just met or are in the process of meeting.