Using authenticated encryption along with signing
Signatures provide one property that MACs don't: non-repudiation. With only a MAC (or an AEAD) any party with the secret key could have sent the message. So Bob could forge a message and claim Alice sent it. With a signature only the party holding the corresponding private key could have created the signature.  MACs authenticate the message, not the sender.
When this property is needed one must accept the performance decrease of adding the signature. If this property isn't needed, then there's no need to sign.