It isn't possible now, but certainly it could be done. The software keeps a history of changes to seating in two places, actually. One is to allow you to undo actions on the Tables tab. The other remembers only what it considers to be "official" seating changes, which are those suggested by the software and confirmed by the user. Those are the changes which show up on the Player Movement screen. The idea is that drag-and-drop makes moving stuff around easy enough that one might do a lot of it just to try different configurations, and you wouldn't want every move to show up as an "official" seating change.
A few details would have to be worked out, such as ...Would there be a switch or toggle that turns on this new "feature", or would it just be the new way things work? Would every player drag be considered a separate move? Or would the first drag start a new player movement session (reset the Player Movement screen, for example), and then every subsequent drag be appended to the list? What would "end" the session? Would it end after a certain amount of time has passed, or would it end when an "official" seating change occurs (the software suggests movement and the player confirms)? Or, would their be, say, a button that starts the session and one that ends it?