The problem is that such "reconstructionism" is just this, a reconstruction, that bears little if any ressemblance to reality, and is grounded on certain assumptions. Someone takes a picture he has of Antiquity, improbably lumps various elements together, and believes to have recreated an ancient world. Religion in ancient Greece was lived socially and was an integral part of the city. Today, it is Christianity which is lived this way--or so should it be. A true religion, a true faith, is something that is lived inwardly, not reconstructed from archaeological evidence. If the Greeks, and the other peoples of the Roman empire and beyond, adopted Christianity, it was for specific historical reasons. Speaking of reconstructing a dead religion is ignoring historical reality, ignoring experiences of individuals and societies that lived in that age, and ignoring the tensions, problems, and solution of this society. You may ignore these, but this is dishonest (also, what do you do with sacrifices? Do you also want to resurect them?).
Much of the ancient culture lives on in popular Greek culture and this is true for much of Europe), so there is nothing to restore.