It's mostly due to how valuable Egypt was in a pre industrial world. The Nile is extremely fertile and can pretty much be the sole breadbasket of a Middle Eastern Empire.
Also I don't really know if it's true that Egypt wasn't "ruled by an obviously home grown establishment till the modern day". I mean wouldn't one be able to make an argument that the Ayyubid Sultanate and Mamluk Sultanate were Egyptian? At the very least early on.
There was also no strong Egyptian identity in the centuries following the Roman conquest. What was an Egyptian really? Greek, Coptic, Nubian, Pagan, Arab, Roman? There was no real answer.
There were some revolts as mentioned during the Ptolemaic period, one during the reign of Emperor Antonius Pius and and quite a few during the early Arab rule (mostly due to heavy taxes, although Arabs/Muslims would also take part in these rebellions). However for most Egyptians Arab rule wasn't really seen as a major change early on. The Arabs allowed Egyptians to be administrators early on, so most Egyptians probably wouldn't have even met any Muslim Arabs early on.
There could be an argument, but for the sake of the thread, lets work as if they weren't.
Thing is, despite its incredible fertility it wasn't able to expand. Now, post Alexander and Persia, it was because it was occupied and surrounded by other groups. But I'd be very curious to see a Post-Ptolemaic Egypt. Perhaps via some sort of revolt that captures Alexandria. Or sooner, an Egyptian revolt on Alexanders death, with Ptolemy instead taking the Levant and Selucius lands further east (there is an ignorance of that period there I feel.)
An alliance between a Free Egypt and a Ptolemaic Syria could be interesting - especially if Egypt modernises its armies via the Macedonian model and adapts to others as well. Its own interests would lead to avoiding as many of the wars it was involved in IOTL, instead selling to the various Greek powers - and perhaps being able to see the politics of the Greater Mediterranean. A Free Egypt as a trading power could well make the move to take advantage of the Punic Wars - allying with Rome, and taking Carthage, and its trade routes, for their own. Perhaps later even adapting to the Roman model of war.
I'll admit, I'm quite enchanted by the idea of a Pharonic refounding of Alexandria, and an overseas Empire of city states trading. It'd be a completely different Med.