The viewfinder is usually not 100% accurate in representing the final image you will get and I've lost a few shots while using a too narrow DOF. I would imagine that cameras, knowing the focal length, aperture and distance to the subject (via focus mechanism?) could compute the depth of field, which would help photographer get better results.
Or as many modern lenses lack hyperfocal distance charts, which are useful for shooting landscapes, it would be useful to have it in camera too, especially since you don't need to know the distance to subject and calculation is much simpler in that case.
Why don't any cameras do this then?
Answer
Some do actually. You are right that most do not though. The main problem is that there is no such thing as an exact depth-of-field. DOF actually depends on the viewing size, actually the angle extent of the image as being seen. Most DOF tables assume a fixed 8x10" print seen as from 12" away for someone with 20/20 vision. Today software allow you to enter these values but you would have to do that for your camera too.
When you switch to Manual Focus mode on a Fuji X100S or one of their mirrorless cameras you see a focus-distance scale at the bottom of the EVF. The thin line is the focus distance and the blue bar shows you the depth-of-field for an unspecified print-size and viewing distance. Notice how when in Aperture priority or Manual exposure mode, the blue bar changes size.
Plenty of DSLRs - above entry-level models - have a DOF-preview button which stops down to show you the image at the selected aperture. This of course darkens the image. Most modern ones can also stop down the aperture in Live-View which make it easier to judge DOF.
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