I can attest that getting one of those cheapo SSD-s for a gaming PC and then downloading games on Steam over a good connection (500 Mbit/s) can overwhelm the SSD and cause the whole system to be unusably slow, with similar multi-second latency numbers being shown in Task Manager on Windows 10. It’s a relatively common situation among the gaming community, I’d say.
Are you talking about a web server running in somebody's basement, or a web server running in a data center? Because the SSDs in a real server wouldn't have SLC caching in the first place.
The OS stops sending bazillions of bytes to the drive, overwhelming its' caches, but waits for the writes to complete. Less throughput from the OS => more time for SSD to complete whatever inner shenanigans are happening.