You could replace the full set of controls with some much more intuitive and integrated click-wheel or touch-screen controls.

Most DSLR's use wheels and buttons to set the most-used parameters (shutter speed, aperture, ISO, focus, AE-lock, etc.). Some have touch screens in addition or instead. However, most photographers want tactile controls so that they can find controls by touch and make adjustments as they work without taking their eye away from the viewfinder.

The thing about intuition is that it often depends on expectations that develop over time. Android users initially find iOS devices frustrating (and vice versa) not because the device is hard to use, but just because it's different from what they've experienced. For photographers, the traditional grip (left hand supporting the body and lens, right hand gripping the right side of the body, index finger on the shutter release) is highly intuitive. And putting wheels, buttons, and joysticks where the right thumb and index finger can easily reach them just makes ergonomic sense.

But a good chunk of photography classes...goes to teaching you how to use the horrible control setup...

Maybe you need to be more specific, but other than the positions of the shutter release and the viewfinder, I see very little commonality in controls between my 1970 Olympus OM-1 and a typical DSLR.

...and backward parameter units such as f-stops.

The units involved have much more to do with physics than they do with the particular sensor technology. The f-number, for example, is a measure of the ratio of focal length to apparent aperture. It determines the illuminance or "brightness" of the projected image for a given scene regardless of the focal length of the lens. That is, for a given shutter speed, if you know you get a good exposure at f/8 with your 50mm lens, you can get a similar exposure with a 28mm or 100mm or 200mm by setting the aperture to f/8. That's true whether you're using film, CCD, CMOS, or glass plates.

There are plenty of good questions and answers on this site that explain specific units; I only want to point out that although digital photography is strongly influenced by a history in which film was pervasive, there's not all that much about modern cameras that's justified purely by that history.

Perhaps the most important influence of film on todays camera is in the sensor sizes. Because digital cameras evolved from their film-based predecessors, they were designed to use the same lens systems. Those lenses have the same sized image circle that they always did, so digital sensors needed to be about the same size as a frame of film. Camera manufacturers had a lot of existing infrastructure for building lenses, and photographers had already invested in lenses, so it made sense to use sensors that could work with those lens systems. But even though that influence is still felt today, it's also diminishing as new systems like Four-Thirds gain traction.