A technique maintains consistent throughput of processing of input/output (I/O) requests by a storage system when changing configuration of one or more Redundant Array of Independent Disks (RAID) groups of storage devices, such as disks, within the storage system. The configuration of a RAID group (i.e., RAID configuration) may be represented by RAID objects (e.g., reference-counted data structures) stored in a memory of the storage system. Illustratively, the RAID objects may be organized as a RAID configuration hierarchy including a top-level RAID object (e.g., RAID group data structure) that is linked (e.g., via one or more pointers) to one or more intermediate-level RAID objects (e.g., disk and segment data structures) which, in turn, are linked to one or more low-level RAID objects (e.g., chunk data structures). According to the technique, a snapshot of a current RAID configuration (i.e., current configuration snapshot) may be created by incrementing a reference count of the current top-level object of the hierarchy and attaching (e.g., via a pointer) the current configuration snapshot to a current I/O request processed by the storage system.