Signed mails do not bring any security first-hand. All they (can) bring is trust in the sender and thus the message. You can use this trust to decide whether it is (in)secure to do whatever with its contents, but it's still your decision.
If an organization of 100 people want to communicate, each pair of them will have to exchange (and maintain!) such keys -- several thousands all in all. Using public-private-crypto, all they need is 100 pairs of keys.
Also, you will be able (or could be able) to communicate with everybody trusting your key (how to achieve this depends in OpenPGP and X.509) and the other knows for sure who you are. For sure. No way to do this without meeting with symmetric encryption.
Also: there are applications where you want to sign, but not encrypt. How to "sign" using symmetric encryption for the public: mailing lists, software packages, ...?
Symmetric encryption in OpenPGP
In the end, OpenPGP is nothing more than a wrapper that puts trust and key management around symmetric encryption which is used for acceptable performance when encrypting (OpenPGP is a hybrid crypto system; public-private-crypto is very expensive for encrypting large data, signing only encrypts a hash sum of the data and thus does not require symmetric encryption).