Dynamic modification of IO shaping mechanisms of multiple storage nodes in a distributed storage system

At least one processing device is configured to detect a failure event impacting at least a first storage node of a plurality of storage nodes of a distributed storage system, and responsive to the detected failure event, to modify an input-output (IO) shaping mechanism in each of the storage nodes in order to at least temporarily reduce a total number of IO operations that are concurrently processed in the distributed storage system. For example, modifying an IO shaping mechanism in each of the storage nodes illustratively comprises transitioning the IO shaping mechanism in each of the storage nodes from a first operating mode to a second operating mode that is different than the first operating mode. The second operating mode of the IO shaping mechanism illustratively has a relatively faster responsiveness to changes in IO operation latency as compared to the first operating mode of the IO shaping mechanism.