There will be far too much damping, to the point that comfort will be gone and roadholding seriously impaired. Coil springs have negligible internal losses and need quite stiff dampers, whereas rubber cones (please do not call then donuts, that has another specific, and correct, meaning on certain vehicles) have a lot of internal hysteresis and only need relatively light damping.
It follows that putting standard dampers on a car with coil springs would be even more unacceptable, as it would bounce around all over the place.
And, just in case someone wrongly concludes from what I said above that you might not need dampers if rubber cones are used, you most certainly do, or you will get knuckle disengagement and suspension collapse, possibly causing a very serious accident, as well as the damping of the cones alone not being sufficient for safe roadholding.