Zillow and Redfin get their listings from the MLS. Realtor.com is run by the NAR.
The practical effect of the MLS has been to rationalize and normalize real estate information across the market.
The downside is that people have gotten the impression that this information just appears. They may be surprised what effects the disappearance of the MLS may have on the market.
Fair enough, forgive my imprecision of terms. But the NAR established and enforces the MLS data and management standards among its member associations that make aggregation and dissemination viable.
I will hazard a guess that the biggest and most active MLS's are run by NAR-associated groups.
I don't see that happening in a world with Zillow, Realtor.com, Redfin, ...