Say you have a PhD in pure mathematics but want credentials for computer science for some reason where it might be necessary (is there such a situation?). Is it a waste of time to also get another PhD in computer science?
An exception might be for professional cases. In medical physics it's not uncommon for people with PhDs in other branches of physics to go through a medical physics graduate program, but I've never seen anyone go through with a second PhD. Usually they either get a post-PhD certificate or a master's degree - enough so that they can go on to enter the profession.
A PhD is largely about learning the skills to research independently. Once you have those, repeating that training is just an excercise in futility. The other thing you get is an in-depth knowledge of a particular field, but there are more efficient ways to get that if that's all you're lacking.
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