If the MLS didn't exist and we relied on private corporate sources of information, then it's likely the experience would be like in France: many competing listing services, none comprehensive.
This is already true in the US; there are multiple things called "MLS", some regional. MLS is a generic term, not a single organization. This is also visible as e.g. Zillow and Redfin sometimes having different listings for one area, because they talk to different MLSes.
Each MLS is franchised by the NAR, which enforces standards and interoperability, and get funds to do it from real estate agent membership fees.
That allows Zillow, Redfin etc. to offer listings free. If they had to carry the weight of all the expenses themselves, it's likely that access to listings would be far more restricted, and/or much less comprehensive.
MLSes are bound by an antitrust lawsuit (that they lost) to provide access to online services like Zillow. I would assume that there is an appropriate payment involved, just like with the MLS's other clients.
I think you're overestimating the costs of running a listing service like this -- there are several hundred companies in the US doing it! -- and underestimating how prone this industry is to inflating costs by illegal anti-competitive practices.
Not saying you're wrong in anything you've stated, but if there are many independent MLS's and it's easy and cheap to set them up, that undermines the whole antitrust argument against the NAR, doesn't it?
If alternate MLS's are easy and cheap to set up and run, and they can provide a much more attractive value proposition than NAR-aligned MLS's, wouldn't the NAR MLS's have been pushed out of existence long ago?
Just running a listing service doesn't mean the local realtors give you listings, that's why the Zillows etc needed to get access to the MLSes that they do use. Getting access equal to other brokers in the area, even if they weren't part of the good ol' boys network, was exactly why there needed to be an accusation of anti-competitive practices.
