What is the advantages to a straight support wall to the slant walls?
It is the result of a "game" that bridge designers play when comparing right-of-way width, travel lane width and median location against the various lengths of standardized stringers (bridge beams). In general, a short slopebank is more stable and less expensive that a retained fill (ergo, retaining wall with fill on the other side). But it doesn't always fit within the right-of-way.
The "slant wall" isn't a wall at all. It's called slope paving. It's there to prevent erosion and simplify maintenance, not to provide any structural support--- the abutment is most likely supported by piles driven into the ground.
There is indeed a structural function to the slopebank beneath abutments, but you are correct that this has very little to do with the abutment structure. In many cases, the approach to the overpass is constructed on fill. There are two means to hold the fill in place: (1) a retaining wall (the OP says "straight wall"); and (2) a slopebank (the OP says "slant wall" and
Tom958 says slant paving, which is more related to the use of rip rap to hold the fill in place).
As this example near Nashville shows, it can be replaced with riprap (pan left to see it) or omitted if the ground is rocky.
Actually, the only way to omit the slopebank or retaining wall atop of solid rock is to construct the abutment further back away from the rockwall face. If you look carefully, the new abutment on the right side is located way back away from the rockwall face (whereas the old abutment was probably located up closer to the edge). Unless it is sheer granite, the rockface is typically unable to support the forces of a bridge abutment (and even if it is, I doubt that a bridge engineer would ever depend on accuracy of the geology data).
Anyhow, this brings me to a nuanced point about how the slopebank or retaining wall actually "assists" the abutments. Due to the normal motion of traffic on the overpass, there is a bunch of lateral forces imposed on both the piers/columns and the abutments. There is also a natural frequency that those structures need to be stiffened against (somewhere around 3 to 10 Hz, if I recall correctly). The lateral width of those structures need to be designed to withstand all of that. Unless, of course, an abutment is surrounded by fill that is retained or held by a slopebank. I might be wrong here, but it is my understanding that in such cases, only the abutment itself needs to withstand the lateral forces and be stiffened against the natural frequency (and not the substructure, which is indeed usually driven or drilled piles).
