HESS, CTA, and VERITAS are used to study cosmic rays.
What they receive are optical (maybe very blue) photons.
So my question is: Why don't we use optical telescopes to study cosmic rays directly?
HESS, CTA, and VERITAS are used to study cosmic rays.
The telescopes in your picture are optical telescopes. They are used to detect cosmic rays using the Cherenkov radiation caused by charged particles moving faster than the speed of light (in air) in the atmosphere. These are normally secondary particles that have been produced in collisions between cosmic rays and nuclei in the upper atmosphere.
Radiation produced by particles moving at close to light speed is beamed in the direction of motion. An array of optical telescopes picks up the beam, and the orientation of the image is a projection of the original track of the particle. By combining images taken with telescopes covering a wide area, and taken at almost the same time, one can reconstruct the paths of the secondary particles to work out which direction the original cosmic ray came from. The intensity of the images tells you something about the original energy of the cosmic ray.
Possibly this is the answer to your question - a single optical telescope might detect the Cherenkov radiation from a single secondary particle, but it would be difficult to reconstruct the path or energy of the original cosmic ray on its own - at least a pair of telescopes, or better still, a network is preferable. The properties of these "cosmic ray" telescopes are also quite different from "ordinary" astronomical telescopes. Cosmic ray telescopes need as much collecting area as possible, because the Cherenkov radiation is faint - but they can do this at the expense of image quality. They use very wide angle cameras (5 degrees or more) and use huge faceted/sgemented mirrors that give massive collecting area, but image quality (maybe 3 arminutes full width half maximum for a point source) that would be completely unacceptable for conventional optical light astronomy.
Or (thanks Conrad Turner) you are asking why we cannot use the mirrors of an optical telescope to focus the cosmic rays onto a detector and image their source? The reason for that is simply that cosmic rays are not reflected from glass/silvered surfaces in the same way that light is. They are extremely energetic particles that either pass straight through the mirrors or are absorbed within them. i.e. They do not reflect or refract in the same way as light.
In other circumstances, cosmic rays are a nuisance when conducting observations with optical telescopes. They are a source of background noise in CCD detetor images. Cosmic rays (or the secondary particles) are capable of liberating electrons in the silicon and therefore simulating small intense light sources in the sky. Often these are seen as small bright pixels, groups of pixels or trails on the CCD image, confusing what you were originally trying to look at. However, these cosmic rays are not focused by the telescope, they are essentially being picked up by the detector itself and would have been so if the detector was not even attached to a telescope at all. They are nearly impossible to shield against because they have very high energies and your detector needs to have a hole to let the optical light in!
Preface: cosmic rays are technically not the main interests for Cherenkov telescopes, they usually focus on very high energy gamma rays and showers from cosmic rays (mainly protons) are considered background in most measurements.
In addition to the very goods points raised in @RobJeffries answer, there are some more reasons why telescopes build for optical astronomy are not commonly used to observe Cherenkov light
Sensitivity and speed of camera and electronics The flashes of Cherenkov light caused by air showers are very faint and short. Their duration is in the order of a few nanoseconds and have only about 100 photons per square meter (exact number depends on energy, type of shower, direction and altitude). To take images of these showers, Cherenkov telescopes use special cameras build of photomultiplier tubes which are both sensitive enough to detect such faint light and fast enough to take images with only about 10 ns integration time. If the integration time would be longer, the noise from the night sky background would hide the image of the shower. Telescopes build for optical astronomy typically use CCD cameras with long integration times in comparison. For example Griffin et al. (2011) state integration times on the scale of seconds or longer (https://arxiv.org/abs/1206.6535). These cameras would not be suitable to make shower images.
Availability The big telescopes for optical astronomy are typically oversubscribed by a factor of 4 (see e.g. https://www.eso.org/public/blog/how-productive-is-the-vlt/). I don't know the exact numbers for all Cherenkov telescopes, but at least for one of them, the oversubscription lower, somewhere in the order of 3, so using an optical telescope seem unnecessary difficult if observation time with a Cherenkov telescope is easier to get. In fact there are studies to do it the other way round and use Cherenkov telescopes for optical astronomy also because of the huge oversubscription of optical telescopes, see e.g. Griffin et al. (2011, https://arxiv.org/abs/1206.6535)