Proper Trap Diameter
There is no problem with the trap being larger, in fact a larger trap and drain line will reduce the chance of a plug. I have found several homes that the vents have gotten plugged from everything from leaves to birds and squirrels getting in them and plugging the vent. If your vent is plugged it may drain quickly for a few seconds then go slow one telltale sign that the vent is plugged or not there, is if the sink drain starts gurgling after the water almost gone or none left in the sink a few seconds later. For an older home I would be looking into checking the vents because that larger line it should drain quickly assuming there is not a big chunk of food waste or grease just below the drain or at the dishwasher T.