I lived in a country that did exactly that. And it was a disaster. The keys were trivially easy to steal, even by accident (personal experience here), and you still have the same trust problem as before, except that with a central authority now you do not have as much control.
I have also used the electronic-signature-comes-with-your-ID-card thing, and it was a similar disaster, with dodgy drivers and half-arsed crypto implementations in common software. E.g., try using the same token in Firefox and Thunderbird (or anything else) at the same time.
PGP is fine. It's just that proper security is not easy. And the same applies in the physical world as much as in computing.