Mouth is correct. The business model for cable boxes is to mass-produce with cheap parts. SSD prices may be "cheaper than ever" but the prices are still more expensive than HDD.
Besides, it wouldn't be just replacing the storage technology but also the storage interfaces (PCIe, M.2), protocols and probably the motherboards to exploit the speed of SSD.
Even if manufacturers started using NAND-based flash memory to read and write data, they'd probably use Embedded MultiMediaCards (eMMC) to keep costs down, which probably wouldn't be noticeably different from a spinning disk.
People see "SSD" and freak out...but there is much more to consider than just the type of drive.