The overflow bridge matters for much more than crowded days. It's extensively used by TM's to get to their place of work without going through Potter, which TMs can't go through unless they are in Potter wardrobe. The only way to get to their work location other wise is to go all the way around backstage, which can/will be much longer than the straight shot through JP.No idea when they'll start it, since there's good arguments for both an early summer start and/or a start after the bridge is built. BUT, an overflow bridge really shouldn't matter, since they're still running the Hogwart's night show on most evenings now, and the bridge is gone. It's tough for crowd control, but a new show can't get the area any more crowded. Anytime I've been back there for the present show, it's shoulder to shoulder crowded with no space anywhere. A new show won't be able to fit any more people in that space, so why wait for the bridge to be built. If they had closed down the present show because of the lack of an overflow bridge, then it would make sense to wait until it's built. But the fact they're still running a show that brings capacity crowds should make the argument for crowd control delaying the start of a new show a moot point.
I feel like I have said this about 5 times now and no one seems to realize that that's been the main use of the bridge.