First of all, - moving is the only function that is specifically different for the "sent" messages. So, the rest of the changes applied to the thread should not be affected, methinks.
Second, - regarding moving, - that should be an option (and better be per account).
I have accounts, where I have "sent" messages stored in the files that correspond to the topic or correspondent, and there are accounts, where all Sent messages are kept in "Sent".
For the former, - I'd use the option "move sent messages from Sent with the conversation chain". For the latter, - I'd use the option "keep sent messages in Sent (while moving the incoming)".
In any case, one has to distinguish sent messages being in Sent and those already filed in a different folder. I.e. if I've moved all the messages pertaining to the conversation to a different folder, and then I am moving the entire conversation to yet a different folder, - the entire chain should go.