Lightning video adapters feature Apple Secure Boot, run Darwin kernel
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This thread has some new information and maybe people will start playing with these more eventually.
To be clear, this just means that the firmware isn't tied to a specific device via the normal ECID/nonce pair like a normal iOS update is.
The real reason this abomination exists is because as recently as 2018, Apple is selling products with a connector that has the equivalent bandwidth of USB 2, not even close to transporting a single 1080p video signal.
The issue that causes poor video quality isn't that Apple chose to run XNU or use an SoC for their adapter, it's that they chose to use H.264 at a low bitrate due to hardware support constraints rather than another encoding scheme which could offer less lossy video.