There have been a few occasions when a trusted CA certificates were compromised and had to be revoked by all browsers. Would that compromise a coins security if it was dependent on CAs?
I don't know but it sounds like a dangerous risk. And even if that wasn't a problem, there would still be the problem of having to rely on third party authorities. Even if only one big trusted authority was used, like VeriSign, there would be the problem of only "elite" nodes being able to operate since the big trusted authority would have monopoly on certificates and could demand obscene amounts of money for licenses. And even with healthy competition among several certificate providers they would have to charge quite a lot of money anyway since they would need to have rigorous control procedures for those who they sold licenses to. And personally I wouldn't even trust a big so-called "trusted" central authority, at least not for a system that's meant to remain robust for centuries.