Egypt a de facto autonomous kingdom, although one that is very closely linked with Palmyra. In fact, a good part of the soldiers that took part in Odainat's siege of the Arg e Bam were Egyptians.
Are they loyal to Palmyra, or loyal to Odainat? If the latter, they could start to become rebellious once a new king takes power and doesn't give the kingdom the attention it wants.
As for the Seven Great Houses, the current situation ironically makes them extremely loyal to the Sassanid dynasty. They know that any kind of serious dissent now will make a future Palmyrene attack much easier to succeed, so even though they aren't exactly fans of the Sasanians, they hate Odainat and his descendants infinitely more. This won't prevent them from pulling all sorts of shenanigans against Narseh and his successors if for whatever reason they start to act like Hormizd IV or Khosrau II.
Interesting. Can't wait to see how that plays out.