Others can speak to it better, but I don't believe they could outright prohibit renting - I believe both FL law and the terms of our ownership provide backstops that would make it impossible to completely prohibit renting. There would also be practical issues in enforcing any prohibition, as we face no limitations currently booking rooms for friends or family that are not renting from us.
Now, Disney could take further steps to prohibit what it considers to be commercial renting (which is very vaguely defined in our governing documents). If they did take some significant actions that made the ownership base significantly less comfortable renting their points, I think it would undoubtedly cause resale prices to fall.
Why? You'd increase supply and decrease demand.
On the supply side, there would be both normal, non-commercial
DVC owners who have occasionally rented out their points and commercial individuals/entities who would sell. If you were paying attention to the
DVC Resale Market, last summer, there was a marked increase in stripped contracts that hit the market after DVC instituted the "personal use" box - this was undoubtedly commercial renters getting nervous about where Disney was headed and offloading some contracts - it appears that was a short lived phenomenon, although that could change if we hear about further actions Disney is taking.
On the demand side, you'd see less demand from those commercial individuals/entities and I think you'd also see less demand from potential non-commercial owners because their ownership would be less flexible. I think a significant selling point of DVC is that it is so easy to rent out your points for those times you aren't planning to use them. Maybe there would be a slight increase in demand from people who had held out buying DVC or who had previously exited because of their frustration with commercial renters and the difficult booking certain rooms. But, I think that would be greatly outweighed by the loss of demand.