The casualty of that solution might be buses (as others pointed out this road is also being used for), but the city can make exceptions for those (as is usual in most places due to stops being commonly in the right turn lane).
It's clear from the massive number of videos, and of various types of drivers (truck rentals, furniture delivery trucks, campers, etc.) that the current "system" they have is inadequate to avoid these crashes. "It just doesn't work". Just blaming the driver only isn't a solution (I actually wonder if the city/railroad has ever been sued because of this).
That is already what is set up. All trucks must turn before going under the bridge.
Except people ignore that and go straight anyway.