Society isn't so simple and black and white that revealing that your top hero is a POS would instantly crumble the hero society. Enji himself may have his hero career compromised and faith in the heroes would diminish as well as their public image but that's not enough realistically, even with the current scale of terrorist attack.
Unlike All Might who was like a pillar, Enji doesn't represent all of the heroes, other heroes have separate images and popularity, and there are already people who dislike Enji in the first place or not care about him.
Furthermore, people and society in general tend to be apathetic towards disasters on a certain level, unless the problem is already knocking on their doors. Yes, there could be protests and so on, debates, and all that, but society will go on and move on, especially with Japan.
For the Paranormal Liberation Front, this is just a step, a huge one, but just one step nonetheless, for Shiggy and Re-Destro to achieve their goal of overthrowing the hero society. I firmly believe Dabi knows this as well, and we all know that Dabi had his own agenda for joining the LOV and now the PLF. And now we know.
For Dabi, destroying the hero society is just secondary. His real and one true goal is going after Endeavor. Stain might've influenced him which is why he still tried to screw over Hawks and the heroes in general, but I'm willing to bet more than likely that Stain just fueled Dabi's outlook of Endeavor further.
Heroes may collapse or not, at this chapter it doesn't really matter to Dabi anymore as he was going to kill himself along with Endeavor.