I like the idea, could lead to a cool battle to look back on / take part in. However even though it is fantasy mineman magic rp setting, I couldn't really see this logically working without the influence of magic over greater distances or without the advantage of high ground. I would take influence from the ESO cinematic. In that one the Daggerfall forces have a similar contraption, but it launches the anchors out ahead of time with the rope, which is then used as a guide as the bridges unravel.
You can see them in action here
This seems like you could logically get much more distance and velocity as you are only supporting the rope during the flight, rather than iron and planks. I see some issues like perhaps the anchors land to far apart for the bridge to fully unravel and of course, that sort of heavy rope is still a lot for a ballista bolt for carry behind it. Either way these bridges should be pretty easy to dislodge, perhaps falling off after a few minutes by gm call from people stampeding across in armor. Could say the planks are extended out onto the guide ropes by crank / spring, not to sure on lore regarding mechanical devices in lotc for that.
Similar to the video, I think any defending force should get once chance to dislodge the attached bridges once before forces get to cross, it isn't a simple contraption and it defeats a large part of a castles defense and should be treated as such. Also make sure to include some anchoring mechanism so the ballista end isn't pulled over the edge when the bridge is used.
Edit: Just realized the art you posted is the lore art for the video I linked, so you may have already intended for it to work this way, I assumed you wanted it working the For Honor way with the bridge flying out all at once