Nothing about Apollo/Saturn was an aesthetic choice. To service aesthetics, the outer surface would be nice and smooth, but there were all sorts of protrusions for things like retro rockets, ullage thrusters, cable conduits, etc., not to mention the corrugated/ribbed fairings between tanks/stages. Note that while the tanks themselves were pressurized, giving them stiffness, the fairings had to provide structural support without benefit of internal pressure; the corrugation/ribs achieves this with minimal added weight.
Everything on the rocket was there to serve a functional purpose.
The black-and-white paint scheme provided visual cues for vehicle orientation. It looks reminiscent of the V2 because it was a good idea both for the V2 and Saturn.
The tail fins provided a measure of passive stability during certain abort modes; engine-out or steering malfunctions could induce sufficient pitch or yaw as to prevent a successful launch escape; the fins would keep this pitch or yaw within limits to allow for a successful launch escape.
Note that only the first stage had fins because it was the only stage that would be operating in sufficient atmosphere for fins to do any good.
When you look at early illustrations and models made to help conceptualize the Apollo mission, they do incorporate a lot of aesthetics, but the final product ended up looking very different. Consider the LM... initial concept models and drawings had it looking neatly cylindrical/conical; compare that with the vehicle that actual landed on the Moon.