First, I can't really help with Formula 1. However, aerodynamics are somewhat hard to do, and there are pretty good reasons why streamlining really does date to the later 1920's, after a very long period of engineers struggling to understand the flow of liquids and gases.

Ship designers had noticed for a very long time that long hulls seemed to go faster than short hulls, and used a rule of thumb for figuring a "hull speed", based on how broad the hull was compared to the length of it. It was rather obvious, too, that water could flow in a nice, orderly direction- which is now called laminar flow, or if going fast could be flowing with lots of swirls and waves- what we now call turbulent flow, and that water mills and turbines seemed to work best if there was less turbulent flow. But it wasn't until 1870 that Osborne Reynolds quantified the characteristics of flow. Reynolds really should be as famous as Edison or Tesla for this, but he was a mild-mannered intellectual who didn't advertise himself. He was hired to be the Chair of the Engineering Department of what would be Manchester University at the age of 26, and stayed there the rest of his life. He was brilliant, but not the best of teachers, sometimes wandering into other areas instead of sticking to a specific topic. If in the process of explaining a problem he noticed a new way to solve it, he might start working it out on the blackboard, ignoring the students sitting there, waiting for him to get back to the lecture…..

He built a test apparatus that let him put a small continuous bit of dye into the flow of water through a glass pipe. He found that at lower rates of flow, the dye made essentially a thin line. But as the flow increased, at some point the ink would stain all the water. This was the point between laminar flow and turbulent flow. In turbulent flow, small vortices or eddies would occur- Reynolds used a periodic electric arc to illuminate them , like a modern strobe, so he could see them better. He discovered that if you multiplied the density of the water times the velocity of the flow times the diameter of the pipe, and then divided that by the viscosity coefficient, if it was over 2,3000 the flow would be turbulent, below that it would be laminar. He then went on to come up with a theoretical model for analyzing that turbulent flow. This was useful in 1870, but when people seriously tried to figure out and build airplanes it became crucially important, and still is.

The later 1800's saw the invention and use of wind tunnels by engineers like Gustav Eiffel ( the guy who built that tower), and lots of things were figured out about wings and lift. But there was uncertainty about how much friction was a part of it- Samuel Pierpont Langley, at the Smithsonian, thought it was irrelevant. But Ludwig Prandtl in 1904 discovered that the effect of friction was to make the air adjacent to the surface stick to it, creating "boundary layer", and that above that layer there wasn't much friction impeding the flow. Within the boundary layer there could be significant shear stress. Prandtl gave engineers a pretty useful way to calculate how much drag was being generated.

Then of course the Wright brothers built planes and other people built planes and tinkered with engines and wings and fought wars with them and made them on an industrial scale. In the late 1920's, a British engineer, Sir B. Melvin Jones, worked with a wind tunnel and a few grad students at Cambridge University to figure out all the drag on many of the current and significant airplanes. He then drew up a graph, comparing the planes to an ideal airplane, and the difference staggered the aviation industry: the Wrights had been flying around at a leisurely 40 mph. World War One had seen fighter planes popping past 100 mph. The Spirit of St Louis had flown at around 120. As the speed had increased, so had the drag, caused by all those exposed radiators and engine cylinders, guy wires, sharp edges. The Armstrong Whitworth Argosy was, in theory, capable of doing 175 mph: loaded with all that drag, it was reaching 110mph. Jones called for “streamlining” and it became the Next Big Thing. Planes became more efficient and so also faster, got better gas mileage. In the hands of designers like Raymond Loewy, it became a fashion, a style, and spread to other things- even locomotives got streamlined.

Though elegant sports cars got streamlined in a fashionable way it’s obvious that race cars got streamlined in a practical way. The monsters of the early days driven by Barney Oldfield were clearly solving the problem by brute force: if you wanted to win a race, mount the biggest engine possible on four wheels and bring along a mechanic. In the 1930’s the race cars had gotten cowlings, rounded edges, tapered tails, etc. But of course a car isn’t like an airplane. You want lift in an airplane, want to go up - because down is where the ground is- but you want a car to stick to the road, not leave it, and maybe that’s why the looks of those 1930’s racers seem to be derived more from boats than from airplanes. But, as I said, I don’t know about Formula 1 and the design history of it: when spoilers were added, etc.

Though aerodynamic engineering got a big boost from the work of Reynolds, Prantdl and others, it would be a mistake to think it got done. Ask any mechanical engineering student what’s the hardest thing learn to solve, and she’ll say turbulent flow- and doing it with a slide rule is harder than with a computer. But part of why that’s hard for designers of planes, boats and ( I expect) cars is that simply reducing drag doesn’t lead to a perfect plane, boat or car. For a boat, the hull with the least drag would be something like a very long, shallow plate pushed through the water edgewise. Very efficient and stable- until you want to turn it in another direction. Airplane designers have had a similar need to balance stability and avoid drag with the need to be able to turn. For bigger ,slower planes it’s not been very, very hard to solve. But for things like jet fighter aircraft, that have to both go very fast and turn very fast, it's harder: Reynolds worked out a way to figure out average turbulence over time- not how to handle the effects of vortices as they quickly come and go. The solution has been to stop trying to create the perfect airplane shape and instead save the pilot from dealing with the constant need to trim the controls in reaction to constant changes in the turbulent flow: to have a computer deal with it instead, what’s called Fly By Wire. But it’s unlikely we will see Formula 1 drivers being allowed to use that solution.

Anderson, J. D., & Anderson, J. D. (2005). A history of aerodynamics and its impact on flying machines. Cambridge: Cambridge University Press.