The Egyptians’ obsession with continuity and permanence is probably rooted in their beliefs. They strongly believed in the afterlife and viewed death as a continuation of life rather than an end. This is reflected in how they prepared their dead. Not only did they mummify the body to keep it from decaying, the buried their dead with necessary things for them to live in the afterlife. This assurance that they would continue to live even after death probably made for a very stable culture because they did not look forward to an end.
Another part of their obsession can be seen in their art. Their canons are consistent for a few thousand years, with one short break. I think they maintained their style as part of their identity. Egyptians seem to understand the importance of stability in culture and find it in the continuity and permanence of their art. Their culture is strong because it did not change. I don’t think they were unaware of this, and that is why they held on to tradition and obsessed over permanence.
What I think is cool is that despite their eventual fall, their identity still holds strong. As a culture they never really died. They capture the imagination and curiosity more so than any other ancient culture.