It's not ICANN in that system, it's the TLD operators, and the problem with that is that for many TLDs and all the most important ones, you'd be adopting a system where your keys are directly managed by institutions we already know to have misissued. The most important TLDs are state-controlled, which is why you saw DOJ notices on piracy sites rather than NXDOMAINs.
And those DOJ notices already have valid certificates today, because the CA racket is just a proxy for the real domain name authority delegated by ICANN anyway.