They can. But it is extremely expensive to do so with such precision. If you need such accuracy there is plenty of scientific grade photographic equipment available on the market as long as you have financial resources the size of a small country's entire military budget to work with.

For creative photography, there is no need for such scientific precision in the cameras we use. 1/3 stop is as close as most of us need to be able to hit. Often, 1/3 stop is more accurate than the equipment we actually use.

Many lenses are not quite as wide at maximum aperture as their specifications claim. Most lens manufacturers round down to the next nearest full f-stop. The same is true of focal length: Telephoto lenses are usually rounded up to the next "standard" focal length and wide angle lenses are usually rounded down to the next "standard" focal length.

There are a few consumer and pro grade cameras and lenses with 'gapless' apertures. Cinematic lenses often have the option to open and close the iris (aperture) in stepless adjustments, much the same way we can manually focus most lenses in steps as small as our hands and fingers can control. This allows "stepless" transitions from one aperture to another while footage is being recorded. There are even a few non-lab grade cameras that can target shutter times in very fine steps. But there is a big difference between targeting specific apertures or shutter times and actually hitting them with a such a high degree of precision.

What would be the point of adding the complexity of the ability to aim for apertures at 1/100 stop intervals if the camera is only accurate to within 1/6 stop? There really isn't one. The same is true of shutter times. What would be the point of adding the complexity of shutter times in 0.00001 second intervals if the mechanical components can't actually be controlled that precisely?

With raw development tools the final image from our creative cameras can be adjusted in very fine steps to compensate for any variation in shutter time or aperture, not to mention the difference between ISO settings and actual ISO used by the camera at that setting. Canon's Digital Photo Professional 4 allows for adjustments to exposure as fine as 0.01 stops, color temperature as fine as 5 Kelvins, color correction as fine as 0.1 mireds along the Blue ←→ Yellow and Magenta ←→ Green axes, and similarly fine adjustments using the HSL tool. Many other raw development tools are similar.

The difference between such cameras used for creative purposes and those used for precise scientific measurements is the degree to which they can consistently hit the targeted aperture or shutter time within a defined very narrow margin of error. This requires the camera to be able to more precisely measure aperture and shutter curtain positions than is required for our creative cameras. Servos for controlling the aperture and shutter movements with such precision are the primary issues from a cost/effectiveness standpoint. That is why many scientific grade optical instruments are based on precise electronic control of the intensity and/or duration of the light used to illuminate what they measure.

For more regarding the technical precision of cameras used for creative photography, please see: Is there a sane reason why ¹⁄₁₂₅ is not, instead, exactly half of ¹⁄₆₀?