The dots are so delicate, with tiny magnet wires and soft plastic that can melt, that it has to be done very carefully. Even with the very best desoldering equipment it would take forever.
Put a hot air gun on the back of the board, and they'll either just drop out or do so with a small poke of the pins.
Care to post a rebuttal? This is a standard practice. I've scavenged many parts this way.
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.
Might not be so bad considering that all the plastic is on opposite side of fiberglass board. When desoldering connectors or smd chips, it's often hard to avoid directly blowing hot air at the plastic bits. That's not the case here. Having dots grouped in rows of 7 makes things a bit more challenging. As it means heating up larger area and increase chance of them getting stuck even when all the solder is molten.
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.