They already have a line of SOC parts for their pro-sumer lineup, Xeon-D. They've never been very popular but have existed for some time, last refreshed in 2019. You could defiantly use them as a desktop. I was trying to get one for my home lab until I just gave up and used a 3700x instead.
When it comes to cost-down; I'd imagine as Alder lake is effectively the cores from a J5040 glued onto another chip, that they will likely refresh Gemini Lake with the new Alder Lake little cores.
I always though Gemini lake presented good value for money, and would like to see something similar on some new boards that don't suffer for the anemic IO/PCIE support as the typical Gemini Lake SOC's had (looking at you asrock!).