A documentary on the Roman empire

[Anomalocaris]

Here's a thought:

Observation: Pain and failure can be excellent teachers if we know how to learn from them. There's a saying, when you succeed, you tend to party and when you fail, you tend to ponder. It's sometimes pain, dissatisfaction, and failure that can inspire people to make changes and ultimately succeed through those changes.

Observation: For whatever reason, Western Civilization was the first to make the leap from an agrarian economy to industrialization. While other cultures seemed content with traditional ways, Europe, or at least parts of it, seemed ready to try something new.

I would offer that it was the catastrophic failure of Western Civilization that we know as "The Dark Ages" that ultimately led to the success of industrialization and that next leap forward for humanity. As Europe was exposed to outside cultures, such as the Middle East or the Far East, it brought into focus how primitive they were by comparison. Old traditional ways of landed aristocracy were eventually cast aside in favor of urban industrial capitalism.

Had European civilization not failed, had Rome endured, would they have held on to traditional ways as other civilizations had. Would Rome have embraced the industrial revolution?

Depending on if Christianity managed to become the religion of the Roman Empire, if not, then yes.

Because Rome did endure in the East as the Byzantine Empire, however it never went through an scientific revolution. Despite having much more access to ancient scientific works than the west had.

That was because the Christians had no interest in ancient science or it's works. Indeed they were opposed to it, there are New Testament verses which condemn science (1 Timothy 6:20 and 1 Corinthians 1:22 for example). This is because they unlike their modern counterparts saw it's discoveries directly contradicting scripture.

You are reading too much into it. It was capitalism that prompted and supported industrial revolution, not the dark ages. West was not the only civilization showing signs of advancement to capitalism before the 18th century. The Chinese was moving along its own capitalist path during 11-12th century. The west was simply lucky in that it was not overrun by the Mongol invasion before capitalism moved very far along.

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It was well into the 18th century before Europe got back to the levels of sophistication it had under the Romans.

Only if your cherry pick the evidence. In the real foundations of the modern world, such as westphalisn state, war, industry, commerce, finance, transportation, knowledge of the world and universe, systematic science, etc, etc the 18th century Europeans were well on the path to modernity compared to whom the Romans would be hopeless iron age yokels.

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The Roman Republic and Empire stifled development. It did not advance anything.

No, it's more like the advancements made by the Romans were too practical to impress the simpleton scribes of the dark ages or to tickle the fancies of the airy romantic. So you underestimate their potential importance.