An interesting thread.
There's no doubt, consumer-level SSDs are surpassing the performance requirements of a camera like the K-3iii. Let's take a lowly 2.5" SATA SSD - with 560MB/sec, writing a 35MB RAW file takes an instant. As for the expected reliability, a 256MB Samsung EVO is good up to 150TB; that's quite a bit more frames than what you could reasonably shoot with a camera
But, would those numbers translate from the PC's context into a camera's? An earlier comment mentioned power requirement. This SSD I've mentioned can get these values by using a lot of "tricks", including a 512MB DRAM/cache and a very smart controller. If you can't do that, everything suffers - performance, reliability. Decreasing capacity makes things worse, too.
At the other end of the spectrum there's the internal storage which isn't much different than of a SD card's. The GRiii has 2GB available (although not simultaneously with a SD card). Good for when you forget your SD cards at home, but not for much else.
I don't really trust those, and yeah they work so well in smartphones... which are devices you'd throw away in 6 months or so
If feasible, I might probably like a "type 1" SSD, fast and reliable, to solve the buffer issues once and for all.
I wouldn't give up on the external storage though. Internal storage would have to be an option, not mandatory.
But perhaps the solution is switching to faster cards (SD or not).