Many of these sites are from the early days of the world heritage scheme and would stand no chance today, but maybe not all of them.
We visited the Minoan site of Akrotiri on Santorini last month - I keep meaning to get round to doing a review. Its absence from the Greek T List runs alongside the failure of Greece to progress the Minoan sites on Crete itself. It is undoubtedly an archaeological site of major importance.
The reason given for deferring it back in 1989 - namely for Greece to propose the entire island of Santorini on both cultural and natural criteria looks very flawed now, particularly following massive tourism developments on the island in the subsequent years. Perhaps the crater caldera and rim might succeed (Akrotiri is in a different area) but one suspects also that the islanders would not want it, given all the accompanying restrictions on further development which would then follow. Akrotiri on the other hand has received major funds to build a state of the art "bioclimatic protective shelter" to protect it following an unfortunate incident in 2005 when the previous low tech one collapsed killing a tourist, and would surely meet authenticity and management requirements.
There are those who are pushing for it - https://www.facebook.com/pg/Akrotiri.Knossos/about/?ref=page_internal