At about 05:55 in Scott Manley's new video NASA Might Be Giving Away A Saturn I Rocket - Here's Why I Love This Vintage Booster he says:
So the Saturn; the first four blockone Saturns, they didn’t have the fins. The block two, they got the fins, because of course this is a rocket by Von Braun.
Why did the block two Saturn I rockets get fins "because of course this is a rocket by Von Braun"?
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.
Wernher Von Braun was in charge of building the following rockets:
The evidence would suggest that von Braun likes rockets with fins. Just to give you an idea, here are a few rockets not build by von Braun in the same time period.
So it was partially a fact of the time, but it does indeed seem like von Braun likes his rockets with fins.
Is it true Von Braun added the fins solely because "he liked the look"?: clearly not.
Did he use them more often than his peers: it's just stats thing at this point but p<0.05 is looking pretty good.
This might be expected as the pros and cons of fins are not a direct/universal trade-off:
Pros: they add stability (and control if they can be actuated).
Cons: they add drag and weight.
If you're struggling to hit dV targets you might see fins as easy weight loss. If you can afford the dV hit, why not?
As to whether this reflects Von Braun's bias, or those of his peers (or is a refection only on the projects and pressures etc those in rocket design are involved in) is hard to tell.
