Who decides who has access to them?
There are probably many who would have ethical questions about this, but tourism is the most profitable industry in Egypt so its not going to just go away. The end of archaeological digs would hurt the Egyptian economy a good deal.
As far as deciding who may excavate the tombs, enter them, or do any archaeological work in Egypt, the Supreme Council of Antiquities usually has the final say. Currently the Director of the Supreme Council of Antiquities is Zahi Hawass, so he usually has the most weight when deciding who may do archaeological work in Egypt.