Hello,
I've tried this same exact thing too many times in the past with many failed attempts and time wasted. The stuttering is somewhat fixable through the collider being larger, but once I added the physics to the bridge, my character started either flying into the air because of the downward momentum the character makes when walking on the bridge would cause the bridge to spring back up, or I would fall through even more.
I think you would be better off faking the physics, which is a lot more work, but would provide more polish. I would put a plane in the shape of the bridge, so if there's some slack in the bridge where it dips down in the middle, make the plane run through the entire bridge. That way, not every box has a box collider.
Where the physics can come into play is if you think the bridge needs to break, create different break point triggers in the bridge and have the bridge break into a broken bridge model with physics on it.
If you're looking for the bridge to sway or wobble during movement, this can be done via animation and I would recommend faking it using invector's physics platform code to keep the player attached/parented. You can think about it in the same way as a player being on a truck/train top while the vehicle is shaking/bouncing as it moves.
Whenever I think about physics in my game, I always look at how BOTW would handle it.
Here's the closest thing they have to what you're trying to replicate I think... (forward to the end where link walks across)
Your example is more like the metal plates, but on a much smaller scale, but imagine a hundred of them under one parent.
I think it would result in physics like Gang Beast or Human Fall Flat. (They most likely have the type of bridge you're working on)
Not sure if I'm being helpful or not, but thought I would give my suggestion!