On the one hand, belief is powerful. By conditioning on assumptions, we can rule out alternatives and move quickly and surely. But belief is risky, especially since all of our beliefs, if stated precisely enough, [are] false. The resolution is that we can use the strength and power of beliefs to better study their limitations.
From a statistical (and philosophy-of-science) perspective, strong assuptions play two roles: First, with strong assumps we can (often) make strong and precise inferences. The likelihood function is a powerful thing. Second, strong assumptions are strongly checkable and falsifiable. We take our models seriously, work with them as if we believe them unquestioningly, then use the leverage from this simulation of belief to check model fit and explore discrepancies between inferences and data.