Air resistance matters, but is only one factor. A much more major factor that a rocket needs to overcome is just gravity - ie marginal mass considerations generally trump marginal aerodynamic considerations. Partly this is a result of engineers having much more ability to control the effects of aerodynamics through launch trajectory/profile design (since aero forces can be controlled by through controlling velocity and altitude, while gravity... much less control).
Here are some factors to consider that generally trend against just "increasing the fineness ratio".
Consider your fuel tanks. Assuming that you have liquid fuel, the static pressure at the bottom of the tank for a given fuel and gravity is purely a function of the height of the fuel column. This means that the taller your fuel tank, the stronger the tank needs to be (at the bottom) to contain it. This will tend to increase your non-payload, non-fuel mass - this is bad.
Similarly, as your rocket gets taller and taller, there is more and more structural mass sitting on top that needs to be supported - ie you need stronger structures.
When a rocket second stage is in vacuum, all of the sudden you want the largest possible nozzle you can get to get the most thrust out of your exhaust. Now having a larger diameter to work with is useful since it's now easier and simpler to have a large diameter nozzle.
Rockets exist to launch payload, which often cannot be shrunk below specific sizes and/or have difficulty being mounted in different orientation. The uh... extra phallic shape of the Falcon Heavy in this case is because the payload fairing needs to be large enough to encapsulate the payload. It's not possible (or really useful) to shrink rocket diameters much smaller than their expected payload.
For a size comparison, the Falcon Heavy's payload fairing is 5.2m in diameter. This isn't particularly a small space, but it's not particularly large either - it's basically exactly the length of a F-150 or two sheets of plywood/drywall stacked lengthwise.