cheaper to just pay the license fee
The problem is that unlike Nintendo, Sony and Microsoft, Valve isn't selling a closed box with proprietary blob.
Their hardware runs Linux with a close-to-upstream kernel(*).
Among other, they are using the FOSS stack: Linux kernel driver, user space Mesa libraries, etc.
All this is GPL meaning that the code is released (or at least pull requests with the latest are wainting to be eventually upstreamed)
And the HDMI's licencing currently prohibits making that code available (or conversly, GPL means that every body should be able to read and modify the code that does HDMI 2.1 shit even people who haven't paid the license).
(*): except for the dock. The Steam Deck's dock has a dedicated chip that does the USB-C DisplayPort to HDMI conversion, so no need to tweak anything on the drivers running inside the SteamDeck.