It depends on how you define camera. In a sense, digital large format does exist, just not exactly in the way we might expect.

There are commercial products called 'Digital Scanning Backs' that fit medium and large format cameras.

Instead of a full grid that can be exposed from one side to the other very quickly via a focal plane shutter, they have one line per color that moves from one side to the other as the image from the lens is continuously projected on the camera's focal plane.

Before we say, "That's not a camera, that's a scanner," let's keep these things in mind:

• They are still a LOT faster than the earliest cameras from the first half of the 19th century. They can be, and sometimes are, used to image three dimensional scenes out in the 'real world'. They can capture a scene at very high resolution in times comparable to a 'gigapan' setup.
• They use conventional view cameras with photographic lenses to project an image onto the camera's back focal plane. Flatbed scanners, in contrast, use microlenses directly in front of the scanning lines.
• Conventional film and digital cameras with focal plane shutters expose the image from one side of the frame to the other (or top to bottom). A digital scanning back is much like a DSLR taking an image at 1/8000 second where a very narrow slit passes across the surface of the sensor in about 1/300 second. It's just that the scanning back does it in super slo-mo.
• Scanning backs avoid the disadvantages inherent in using a Bayer-masked sensor.

They're often used for high end art reproduction. But they are also used to image static scenes.

The reason digital cameras with Bayer masked grid arrays don't exist in large format sizes is primarily one of cost. It's not just that a sensor 10X as large costs 10X as much. Such a sensor would cost many more times that! The smaller a sensor is, the more potential chips can be made from a standardized silicon wafer. But there are always errors in the billions of transistors on such a wafer. If I can cut 100 chips from a wafer and there are 15 errors, at most I lose 15 chips and can still use 85 of them. Chances are good that at least a few chips will have more than one error and I may get 87-88 usable chips. If I'm only cutting the wafer into 4 pieces, things get a little more difficult. If there are an average of 15 errors per wafer, I might have to go through a stack of several blank wafers to get a single usable chip from them!

For more about silicon wafer utilization, please see:

Why does increasing sensor size necessarily lead to lower silicon wafer utilization?
Why did camera manufacturers create crop sensor cameras?
What limits the size of digital imaging sensors?
Where does the price premium of full-frame come from?