What about Akrotiri as Minoan site?
Well Greece tried with Akrotiri way back in 1989 and it got deferred - so that is 2 of the "Top 10 missing" which UNESCO had the chance to inscribe but decided not to at the time (with Ephesus)!!
This PhD paper by a Greek student considers what the Greek inscribed and tentative lists tell us about how Greece has seen itself across the time of the WH scheme (and on how the rest of the World sees Greece!). It may be of interest in showing the approach which Greece had been following. It predates this latest T List of coursehttp://www.academia.edu/1541649/Heritage_in_Greece._The_national_narrative_told_by_th e_Greek_World_Heritage_List
He wasn't (page 40) able to shed much light either on why Akrotiri got deferred nor on why Greece has never pursued the matter further . For the original referral he should have looked at the Bureau meeting report Page 8 - it wanted the whole island inscribed! See http://whc.unesco.org/archive/1989/sc-89-conf003-12e.pdf
Note that it states that Oia and Phira were on the Greek T List at that time - I presume they must have been removed at the time of the next T List?
Considering the site's possible credentials on Natural Criteria - this extract of a book from 2013 considers the situation regarding the inscription of Volcanic sites around the worldand quotes an older comment on the number of iconic ones "missing" including Santorini - Etna and Mt Fuji from that list have since been inscribed so it could be that UNESCO is likely to be a bit unimpressed with the Volcanic potential of the site. See page 229 ofhttp://books.google.co.uk/books?id=1R18AAAAQBAJ&pg=PA229&lpg=PA229&dq=santorini+world +heritage+unesco+tentative+list&source=bl&ots=H7YRYrE4Se&sig=vyUqA7LsMsw8OgB7-O6_hVCA m9k&hl=en&sa=X&ei=FJkwU8PoNYq2hQfPpYDIAw&ved=0CGcQ6AEwBg#v=onepage&q=santorini%20worl d%20heritage%20unesco%20tentative%20list&f=false