Just to be precise, third person pronouns are in fact not personal but rather anaphoric. That is, they refer back to another linguistic unit. The first and second person pronouns are 'personal' in the sense that they refer to the (nominally) two direct participants in a conversation. They are also different from third person pronouns in that they do not exhibit gender distinction, and they are deictic. That is, their meaning depends on who the speaker is.
Having said that, Homeric Greek used the demonstrative forms ὁ, ἡ, τό (including the nominative) as a third person pronoun (he, she, it), and as a demonstrative pronoun (this, that), and as a relative pronoun (who, which). It is often a point of difficulty for those just beginning to study Homer. This also certainly ties in with what Paul said.
So why have nominative forms of first and second person personal pronouns? The Greek grammar books all tell us that they were used only to provide emphasis. I would say it is a natural feature of discourse structure to want to emphasize speaker versus listener or vice versa. The verb endings already indicate the category of person (as a nominative case equivalent) so the separate nominative pronoun merely reinforces the idea.
Marking a non-participant in the conversation, third person nominative markings are only in the verb endings because the referent does not represent an active role in the discourse and so has no need (desire?) of emphasis.