Canvas is AGPL licensed. Moodle is GPL. Universities or anyone else can already contribute to big name LMS.

Canvas is used by Harvard, MIT, Stanford, Carnegie Mellon, CalTech, etc. If they each paid 10 FTE, they could set up a foundation that could govern the development of a top-tier LMS. Every tier-1 state institution could contribute 5 FTE. Even little JuCos could chip in an employee here and there. You'd pick up hundreds of capable employees at a fraction of what those schools currently pay to Instructure.