It was only a couple of months ago that Yahoo lost control of the data of 500 million people and now we’ve learned of another, much larger breach, that took place in 2013. The attackers stole names, dates of birth, telephone numbers and answers to security questions for a billion accounts. Yahoo is not a safe place for your data.
It is important that you do not close your account fully because the complete bastards at Yahoo allow new users to register previously used account names. This could leave you vulnerable if your email address was used as a recovery option somewhere. I closed my account a couple of years ago without knowing this.
Email is important. It is often the link between your online identities. If an attacker secures access to your email, everything else should be considered compromised.