The highest density storage is currently 1PB in 1U, fitting 40PB in a Rack. We expect to reach 100PB in 2025, with some futuristic roadmap of 200PB in 2030, assuming we could yield those NAND. And a thousand layers NAND to reach 500PB in 2035.
That is still an order of magnitude smaller than 16EiB. So no, not in a few years time.
One thing is storage density, another is data transfer rate.
Frontier's LustreFS based mind-boggling 700PB Orion storage subsystem writes at a similarly impressive 5TB/s [1]; so with a generous reading, it could potentially fill up in about 39h. Historically, disk density increased more rapidly than network bandwidth, which ultimately limits the performance of distributed file systems.
If it takes weeks or months to write such enormous data set, then there will be only few use cases, if it takes years there will be none.
That is still an order of magnitude smaller than 16EiB. So no, not in a few years time.