When an entity $A$ wants to send a message to entity $B$, he can attach a MAC to the message. Entity $B$ on receiving the message can use the pre-shared key to compute the same MAC and confirm if the message is untampered with.
This approach protects $A$ and $B$ from an external attacker who might want to mess with the message. However, it does not protect $A$ from $B$ or $B$ from $A$. For example, $A$ can craft a message and claim that it came from $B$ since $B$ is the only entity that shares this particular key with $A$.
Digital signatures eliminate this problem, since the MAC is replaced with a hash which is encrypted with the senders private key. Usage of the private key means that $A$ and $B$ cannot deny or forge messages between each other.
Which brings me to my question. Why do MACs continue to be so relevant when they are susceptible to the kind of attack described above? Under what circumstances would one prefer a MAC to a digital signature?
Note that I have been made aware that there is a question on here which seeks for a comparison between MACs and digital signatures. That question is different from mine since I am looking for concrete cases where MAC would be used instead of digital signatures. Can someone quote a protocol, application, etc, where the disadvantages of the MAC relative to digital signatures can be ignored?