Its probably more likely any consolidation would happen with the smaller players (NBC, CBS) doing this with Netflix rather than Disney.
Most interesting to this particular discussion is that Disney themselves have a white label platform at this point. Disney Streaming powers Disney+ and others at Disney, started as the pure white label platform from BAMTech (which Disney acquired), has merged in some of the platform used by Hulu as well (and Hulu had some white label deals beforehand, to my understanding) and is still the white label powering things like MLB and NHL streaming services (which both used to have small amounts of ownership in BAMTech, but now Disney is sole owner).
If Netflix were to build a white label platform today, they'd already have Disney as competition.
Like, Netflix's UI has some annoyances, but it would be so much better if I could access all my streaming content in one central place instead of having to manage a dozen different shitty services, all with their own separate accounts, apps, watch lists, etc. and their own idiosyncratic quirks and buggy (or outright missing) features.