Pierre-Loup Griffais recently re-tweeted NVK progress with enthusiasm, given that he used to work at Nvidia on the proprietary driver it's replacing I think it's a sign that Valve wouldn't particularly want Nvidia's driver even given the choice, external bureaucracy is something those within the company will avoid whenever possible.

Going open source also means their contributions can propagate through the whole Linux ecosystem. They want other vendors to use what they're making, because if they do they'll undoubtedly ship Steam.