There are a few different "account" types in an Android phone. One is the google account. Another is the email account. One isn't the other. You can add or delete one type without affecting the other types.
If you want to remove your email account, remove your email account, don';t remove your Google account. That's the one you install apps and music with. Email is strictly to receive and send email, and you handle that in your email app. (When you first set the phone up, it asks for your Google account, then adds that address to your email app. But they're not the same thing.) If you had a google Voice number on the deleted Google account, or installed any apps using the deleted Google account, you should add it back - under Settings/Accounts, not in email.