From this Kurzgesagt video, they mention that every bronze age civilization near the fertile crescent were destroyed by mysterious invaders, aside from the ancient Egyptians.. They mention Mycenae, Hittite Empire, Assyria.
What are the theories out there about the fall of these civilizations? Any recommended reading about the end of the bronze age?
Take a look at the AMA with Eric Cline, author of 1177 BC: The Year Civilization Collapsed, which discusses a lot of the issues around the end of the Late Bronze Age. Also see the superb set of posts by u/Daeres in What happened to the Mycenaeans?
I provided a list of recommended readings in Any recommendations for Bronze Age Collapse?
It is wholly inaccurate to say that "every Bronze Age culture except Egypt was destroyed" and "writing and progress froze for hundreds of years" as the linked video asserts. The Hittite empire fractured into smaller kingdoms, much like contemporary Egypt did during the Third Intermediate Period, but many aspects of its culture survived in the form of the Neo-Hittite (or Syro-Hittite) kingdoms of the Iron Age, the rulers of which were direct descendants of the Hittite kings of the Bronze Age. Notably, the region was still referred to as Hatti by the Assyrians long after the Bronze Age. From a boastful account of Shalmaneser III (858–824 BCE):
I have made the Hittite sovereign bow down at my feet; now let me go and see how the Urartians fight!
Other regions like Elam and Assyria survived into the Iron Age as well. I discussed the history of Assyria before and after the Bronze Age/Iron Age transition in Why is it called the Neo-Assyrian Empire and not just the Assyrian Empire?