re: Why do people believe Saban would have built a dynasty if he had stayed at LSU?

This is intended as an Alabama ego stroke and nothing more. They want to think and prove that they are just inherently better than everyone else, not that they literally have had the two greatest coaches of all time run their program for extended periods. The fact of the matter is this, Alabama is no more immune from lulls than any other program similarly situated in terms of natural resources. It depends on who is coaching at that time. Look at UF under Meyer and UF now, for example. Their natural recruiting footprint and financial resources are not at this untouchable exalted status.

Here is where I will give Alabama credit. They have created a culture of demanding and expecting excellence. That's where they gain the advantage over similarly situated schools in terms of natural resources, e.g. Florida, UGA, LSU. The latter schools don't quite demand it as much as Alabama expects it. This is what gets them to go out and hire elite coaches and stymie any lull they may experience.