A storage system comprises a plurality of enclosures and a storage controller. Each enclosure comprises at least one processing device and a plurality of drives configured in accordance with a redundant array of independent disks (RAID) arrangement. The storage controller obtains data pages associated with an input-output request, provides the data pages to a processing device of a given enclosure, and issues a command to the processing device to perform at least one operation based at least in part on the data pages. The processing device of the given enclosure receives the data pages from the storage controller, generates compressed data pages based at least in part on the received data pages, stores one or more of the compressed data pages on the plurality of drives according to the RAID arrangement and returns information associated with the storage of the compressed data pages to the storage controller.