Even more importantly, over time a sagging roof that holds water will sag more due to the weight of the water and being a "universal solvent" standing water degrades most materials.

At best, you will probably get leaks. At worst, catastrophic [1] structural failure.

On the other hand, reroofing can be relatively expensive [2] and disruptive and rope is cheap and everyone has their own risk tolerance and budget.

[1] "catastrophic" in the engineering sense of material failures.

[2] Particularly fixing a fundamentally flawed design. And standing water is a symptom of a fundamentally flawed design.