The JSB isn't even the bottleneck. It's the crazy myriad of lights at Pandora/Johnson and Store.
Thing is, how else would you do it?
There's room for a proper roundabout there but probably too much traffic at peak periods for a roundabout to be functional. The bridge doesn't line up properly with either Pandora or Johnson so having a simple 4-way at the end of one of those streets doesn't work; and you'd end up with two lights on Store/Wharf - one at Pandora and one at Johnson. Further, traffic in one direction (depending which road you lined the bridge up with) would have to turn on to Store/Wharf for a block to get on or off the bridge, causing a further bottleneck.
The absolute worst option would be to have three T junctions - Pandora-Store, Johnson-Wharf, and the bridge-Store/Wharf (I don't know where the street name changes) - meaning three very close together lights on Store/Wharf and all bridge traffic having to make two turns. Blech!