A loss of trust in the CA system by the general public would likely lead to a loss of trust in the internet in general.
Edit: I mean, I can see how it's in the browser's interests to convince people that the system is reliable. And I can see how it's in web companies' interests to convince people that the system is reliable. But trying to convince people that the system is reliable when it is known not to be reliable strikes me as ethically questionable, at best.