I was moved recently without notice when boarding, seemingly with no justification other than "operational reasons". My seat had been changed by BA 3 times prior to the flight with no notification. I spoke to BA about why they do this and they advised they are working on a system solution to notify customers. A BA IT project.... sounds fun.
A couple of years back Mrs Y and I were moved from the front row of Y on the NCE-LHR route (was a 767) to almost the back row. It was a Saturday morning flight and I reckon there were no more than 50 passengers in Y. And our original seats were empty.