The more boring explanation: Egypt wants to control the exploitation of Pharaonic material culture under their control, which they consider their cultural patrimony. If they can't do the tests and get the glory, they don't want others to do so instead. For an example of this, see Hawass' decision preventing foreigners from doing DNA testing of mummies in Egypt, dismissing it as useless, followed by him personally publishing such work a decade later.

In any case, there is plenty of Old Kingdom material in foreign museums that is available for testing.