Nah, very little of congestion is trucks. You can even see that in this picture. Plus, you're not trying to make driving easier, that will just cause more people to drive (one more lane bro). You make everything else easier and people choose to walk/bike/bus and the roads clear up because there's fewer people choosing to drive.
Buses and trains. That, or spaghetti interchange that are bigger than the rest of the city. Also, replace key arterial roads with a pedestrian path, call that path a park, and charge $20 for entry. That will easily fund all the city services and nobody will be too inconvenienced by having to pocket their car as they walk across the "park" to get between neighborhoods. Now excuse me, I have to go murder a little blue bird that won't shut up about the garbage piling up