Page Sizes (SSD)

Yes, there are SSDs with 8K or even 16K pages.

Coding for SSDs – Pages, Blocks, and the Flash Translation Layer - Code Capsule says though that it isn't practical to ram it up just for the heck of it:

• as page size grows, so does write amplification (the term's also explained on the link)
• NAND memory is rather slow by itself; striping and streamlining is needed to compensate. Larger read granularity makes this harder.

Thus, they apparently balance it to keep the number of pages/blocks/etc manageable for very large SSDs (the 1st linked article talks about 480GB and 960GB(!) ones).