I have concentrated more on the "what" than the "why". The "why" is much more difficult, but I can offer some suggestions.
1) Israel was traditionally part of the Egyptian territory, so the ancient history of Israel is Egyptian history. However, there were obviously other motives involved in writing the Old Testament narratives as they did.
2) The Jews that returned from Babylon and Persia to found a new temple in Jerusalem naturally wanted to carry their history with them, but naturalize it to their new home (Jerusalem in Israel rather than Thebes in Egypt). Pilgrims have always done this.
3) There was also the need to protect themselves. One did not go about boasting of royal standing when one did not have the army to back it up.
4) They had to honor the terms of their resettlement. Those likely included a prohibition of political activity with Egyptian satraps or even traveling to Egypt.
5) Perhaps the most significant element was one of philosophy. The Jews in New Jerusalem had taken a strong anti-kingship stance. The Old Testament preserves their heritage from a royal family, but without directly associating it with greater kingship of the pharaohs. And indeed the Persian Great Kings were still ruling as pharaohs over Egypt during the Persian period.
I think most of these points are covered in the book abstract:
© Charles N. Pope, US Library of Congress. All rights reserved.