1. In data storage equipment which includes a set of physical storage drives and storage processing circuitry which is constructed and arranged to access the set of physical storage drives, a method of processing input/output (I/O) requests from a set of host computers, the method comprising: storing, by the storage processing circuitry of the data storage equipment, a set of storage drive objects in main memory of the storage processing circuitry, each storage drive object among the set of storage drive objects including (i) a storage drive data area; and (ii) a zeroed chunk table, the storage drive object representing a respective physical storage drive among the set of physical storage drives, the storage drive data area including an identifier that uniquely identifies the respective physical storage drive, the respective physical storage drive including (i) a data region and (ii) a metadata region, the data region being divided into a plurality of storage chunks, the metadata region including a plurality of metadata areas associated with the plurality of storage chunks, respectively, the plurality of metadata areas containing a plurality of status indications of the plurality of storage chunks, respectively, the zeroed chunk table including a plurality of zeroed chunk table entries corresponding to the plurality of metadata areas, respectively; marking one or more of the plurality of status indications contained in the plurality of metadata areas to indicate that one or more of the respective storage chunks must be initialized to zero before use; having marked the one or more status indications contained in the plurality of metadata areas, marking one or more of the plurality of zeroed chunk table entries corresponding to the respective metadata areas containing the one or more marked status indications; receiving, by the storage processing circuitry, I/O requests from the set of host computers; and performing, by the storage processing circuitry, I/O tasks in response to the received I/O requests, the I/O tasks including zero on demand (ZOD) operations pertaining to the respective storage chunks, the performing of the ZOD operations including: making determinations as to whether any of the respective storage chunks must be initialized to zero before use by identifying the marked zeroed chunk table entries corresponding to the respective metadata areas containing the one or more marked status indications; having identified the marked zeroed chunk table entries, performing the ZOD operations on the one or more respective storage chunks indicated by the marked status indications as requiring initialization to zero before use; and having performed the ZOD operations on the one or more respective storage chunks, (i) unmarking the marked zeroed chunk table entries included in the zeroed chunk table, and (ii) unmarking the marked status indications contained in the plurality of metadata areas included in the metadata region of the respective physical storage drive.