Maybe eventually, but Valve don't tend to update their hardware very often so it'll probably be a while. They went over 6 years between their last VR headsets, and the Deck is over 3 years old now with no hint of a successor coming (the OLED version is more recent but that was a minor iteration with mostly the same specs).
I care a lot more about the screen resolution than the chip. The Steam Frame would make a really cool Linux workstation if the pixels per degree on the display matched typical monitors. Unfortunately, the resolution would have to be much higher than it is.
The 8 Gen 3 also still uses the previous tile-based A7x GPU architecture, while newer chips use the "A8x family of GPUs based on the new Slice architecture".
