Signatures in e-mail are like the final chord in the symphony. Short but essential; it does have an importance.
Imagine yourself being a pianist playing at some musical competition. You play like Mozart in his 7 years, and everything is going great, but suddenly you falsely played the very final chord. Applause will come (because the audience is polite) but the first prize will go to somebody else.
Similarly, an email signature is crucial to nailing that first impression.