A technique operates multiple data storage tiers including a solid state drive (SSD) storage tier having SSD storage components and a hard disk drive (HDD) storage tier having magnetic disk devices. The technique involves establishing write quotas for the SSD storage components of the SSD storage tier. Each write quota identifies an amount of data that is permitted to be written to a respective SSD storage component during a predefined amount of time. The technique further involves consuming the write quotas in response to write operations performed on the SSD storage components of the SSD storage tier. The technique further involves, in response to a particular write quota for a particular SSD storage component of the SSD storage tier becoming fully consumed, performing a set of remedial activities on the multiple storage tiers to protect operation of the particular SSD storage component of the SSD storage tier.