The plastic is likely the problem there. It's quite easy to melt the plastic on parts like this and if it's thin, has a low melting point, and needs to function mechanically it's likely to do more damage than with your average chip package.
But the theory would have to be tested and there aren't many people with so much flipdot panels that desoldering is a major concern. And ones who have few some don't want to risk it. So bulk processing techniques are likely underexplored.