Based on what you said, you didn't actually look at HDMI protocol, only the protocol exposed to your HDMI encoder chip. You could have such a protocol on Thunderbolt 3 encoder chip.
FWIW, yes HDMI is still pretty simple, but not as simple as you describe it. Even though there are 3 pairs of data it's not one pair R, one pair G, one pair B (highest-bandwidth HDMI uses 4 pairs), it's just one data bus. The data pairs aren't only used for data colors, but also conveys audio, and info frames (which will include various stuff like HDR or VRR metadata). Of course there is the matter of DRM: the content will often be encrypted (but negotiation of that encryption happen separately, over I2C)
FWIW, yes HDMI is still pretty simple, but not as simple as you describe it. Even though there are 3 pairs of data it's not one pair R, one pair G, one pair B (highest-bandwidth HDMI uses 4 pairs), it's just one data bus. The data pairs aren't only used for data colors, but also conveys audio, and info frames (which will include various stuff like HDR or VRR metadata). Of course there is the matter of DRM: the content will often be encrypted (but negotiation of that encryption happen separately, over I2C)