Part of it is safety-driven, which was the primary reason for the twinning of the bridge portions. Another part of it is condition...the Thimble Shoals portals have had some cracking. Lastly, parameters have changed from the previous plan for a parallel Thimble Shoals tunnel to a brand new 4-lane tunnel there because of a desire from the Navy for a deeper Thimble Shoals channel. The current tunnel plan would support a deeper channel.
Regarding bottlenecks at the tunnels....they aren't significant, but in my (extensive) experience, there are two things that can happen that are technically considered bottlenecks: A) platoons of traffic lining up behind someone driving slow through the tunnels. I've personally been stuck behind timid drivers who will barely go 30 through the tunnel, and by the time we clear, there's a few dozen vehicles (including trucks) lined up behind the lead vehicle; B) incidents, whether a crash, maintenance inside the tunnel, or the need to stop traffic in both directions for an oversize/permit vehicle, can easily stop traffic for a half hour or more.