Those parts competed with the RX480 with 8GB of memory so NVidia was behind AMD at that price point.
AMD had not been competing with the *80/Ti cards at this point for a few generations and stuck with that strategy through today though the results have gotten better SKU to SKU.
And you’re quite right they don’t want these chips in the data center and at some point they didn’t really want these cards competing in games with the top end when placed in SLI (when that was a thing) as they removed the connector from the mid range.
Without the extra VRAM, it takes hundreds of times divided by batch size longer due to swapping, or tens of times longer consistently if you run the rest of the model on the CPU.
But if you just want to double the memory without increasing the total memory bandwidth, isn't it a good deal simpler? What's 1 more bit on the address bus for a 256 bit bus?
Instead, it appears entirely possible to double VRAM size (starting from current amounts) while keeping the bus width and bandwidth the same (cf. 4060 Ti 8GB vs. 4060 Ti 16GB). And, since that bandwidth is already much higher than system RAM (e.g. 128-bit GDDR6 at 288 GB/s vs DDR5 at 32-64 GB/s), it seems very useful to do so, though I'd imagine games wouldn't benefit as much as compute would.
You can see this with overclocking VRAM. Greatly benefits mining, slightly or even negatively benefits gaming workloads.
This extends to system RAM too, most applications will see more benefit from better access times rather than higher MT/s.
The RTX 1060 came with 6GB of VRAM. Four generations later, the 5060 comes with only 2GB more.
I suspect NVidia does not want consumer cards to eat into those lucrative data centre profits?
The cost of 1GB of VRAM is $2.30 see https://www.dramexchange.com