The standard motte-and-bailey is framed as a move on the part of the party making the claim (let's call her Alice). But I think things that look like a motte-and-bailey can often be the result of the conversational partner (Bob) not making it safe for Alice to concede that her original point was fuzzy or too strong. If Bob will treat Alice's updating/saying "You're right, my claim is too strong" as proof of lower status, then the motte-and-bailey move (to backtrack and state she was not trying to make the stronger claim to begin with) becomes much more available and attractive as an option, as it lets her save face/keep status.
This predicts that we would see more motte-and-bailey dynamics in adversarial public discussions where the outcome of the debate amounts to an exchange of status or power, and should be rarer in cases where status is already settled, or in high-trust environments.
From the few times I managed to reflect and catch myself during conversations, I usually do motte-and-bailey without realizing it. It is motivated reasoning from wanting to prove myself correct quickly.