They charge a fee for access to the spec and maintain who can claim their products are HDMI compliant and require compliance testing on those products.
An open source implementation would make that spec public and strip a lot of control they hold.
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HDMI Forum has fewer than 80 members and membership fee is 15,000 USD/year. Valve could spin up 80 companies, have them join the forum for a low low price of 1.2M USD and outvote remaining members to open source the entire spec.