What's the advantage of this over a simple hardware interface (which should be really simple since I thought NVMe was basically just a PCIe node) that directly exposes the flash and then let the application/filesystem/whatever layer handle it?
The error rate of raw flash is incredibly high -- it takes loads of error correction to make it reliable, especially with modern MLC and QLC memories -- and the structure of flash erase blocks means that it doesn't support random-access writes. A proper flash translation layer, implemented in hardware, means that software can forget about all the strange features of flash and use it as general-purpose block storage.
And SSDs already abstract that without adding a key-value store on top of it.
Managing 16MB of SLC NOR flash is trivial for a 580MHz MIPS core with 32MB of DRAM. Managing 16TB of TLC NAND is completely different. There's a reason that SSDs almost always have 1GB of DRAM for every 1TB of NAND.
It's telling that high-end embedded Linux devices, like Android phones, typically use storage devices which implement their own translation layer, like eMMC or NVMe devices, not raw flash.
You may need a basic background in solid state physics for some parts.
Or perhaps the h.264/h.265 codecs built into modern CPUs and GPUs?
And this isn't at all a new phenomenon, either. We've been using accelerators and coprocessors (as they were often originally known) for decades.