I think this cartoon was intended to be ironic but it really shouldn't be. All those who are in the helping professions and who practice intense interaction with others need to have someone to talk to regularly themselves. I'm not sure why this isn't universally obvious because it is simply good mental and emotional hygeine. Those who repeatedly hear the stories of trauma survivors particularly need to process that material with someone skilled in listening.
I, personally, would not dream of doing the kind of work I do if I did not have an ongoing relationship with a therapist. I think that would be irresponsible - even unethical. If I were an accountant or a researcher or the like, it would be different. But every day I listen to people who are experiencing some kind of emotional suffering or, at the very least, confusion. If I don't take the responsibility to process how that affects me as well as to heal and transform my own pain, I'm likely to transmit it to others.