If the mower sucks it up, it was too dry to cut in the first place. Think about the question. How would it be better to cut a completed circle, leaving no roots attached, as opposed to digging a horshoe shaped flap and leaving at least 1/4 of the piece intact? I don't think the mower 'sucks' it up. If the mower is traveling the same direction the flap would lay when opened, it will pull it up and away from the earth...unless you left some soft soil under the plug and pushed the root system down into the soft dirt. If the mover is traveling the opposite direction the flap is cut it will tend to just push it back down. There's also a difference between what a reel type mower will do compared with what a rotary mower will do. Obviously the smaller the cut area the less likely something is going to disrupt it. Most mowers used in parks and schools do not have vacuum attachments to catch the grass. Takes way too much time to dump it. They use a mulching blade that chops the grass up finely and the soil uses it to fertilize the growing grass. It also retains the mositure better that way.
I asked about 10 professors from major univerities about how to best prevent damage. They were all professors of a 'Turf Science Program' and a couple were darn right astounded that we metal detector folks would even give that a considereation. The best remedy to keep the grass intact is to water it after you dig it. Not likely! Water weighs 8.5 lbs/gallon and the amount you'd need for 5-10 holes would be a whole lot more than your camel back water supply. A good idea but not practical.
How about limiting digging flaps only when the ground is damp, if in a park or school, and when it's dry just go after the shallow stuff with a coin popper of some kind?? All summer, I hunt shallow and only carry an Ice-pick and a homemade coin popper. I dig a lot more of the target in the foil and pull tab range hoping for a ring. If it's a shallow target, like 3-5" it's not that tought to do and is a lot better for the grass on the field. I am afraid that without some self-restraint with our collective 'plug' making, soon everything will be closed to us except private property. jim