The CA model was never designed to do more than support Internet commerce. It was designed to be secure enough to exchange credit card information.
CAs are not useless against defending against intelligence services, they are only vulnerable to being suborned by a limited number of such agencies, the ones that they have plant in. And any defection is visible on the Internet. Hence the use of schemes such as Comodo CertSentry and Google's Certificate Transparency which are designed to prevent covert subornation of a CA by making the results of the attack visible.
One of the many reasons security is hard is that you have to defend against all the attacks, not just one particular one that someone is obsessing about. Nobody has proposed a replacement for the CA model that works as well within the existing constraints.
Peter Eckersley proposed a scheme 'Sovereign Keys' that solves the hard problems of PKI by pretending that the system administrator will never ever make a mistake. Moxie's 'Convergence' is three years old now and we are still waiting for an actual written specification. The problem with Convergence is that it depends on a notary infrastructure that doesn't have a business model. So it is hard to see how the world of commerce is going to be keen on moving to an infrastructure that we know will have scaling issues.
The CA model isn't prefect but it is the only part of the Internet security apparatus that fails rarely enough for the failures to still be news. McAfee fails to spot viruses on an hourly basis. There are serious security fixes for Windows, OSX and Linux every single month. Those don't make the news because they aren't news any more.
The market for the proposals that are 'stronger' is essentially the same as the constituency that use PGP every day and use Tor and keep their money in BitCoin. It is not a negligible constituency but the people who are in it have to spend about a quarter of their waking moments managing their security.
Web of Trust isn't perfect either. Choosing between the two is pointless because neither meets every need that the other meets. So instead of having the argument over which one to pick we should work on ways that let people use both in a seamless connected fashion.