There are two fundamental types of interviews that have entirely different goals. One is the interview as entertainment and the other is interviewing someone to get important information about a specific thing on the public record. And the styles are very different. Sure, sometimes it's fun to listen to a random famous person reminisce for hours about random stuff that's happened to them in an unstructured way, but I don't really consider that an interview. Most of the time I'm not there to see the interviewer or the guest for their own sake, but to try to learn something about an important question.
To me a great interviewer is someone who can get to the heart of the issue at hand and elicit an interesting and enlightening answer to an important question as efficiently as possible, especially when it is a question person really doesn't want to answer. Sometimes it does take hours to get there and that is fine, but if you can get answers you are looking for in 15 minutes then there is not no need to waste anybodies time and just let your guest ramble about whatever is one their mind.
You're talking more about a legal cross-examination. Or a police "interview." They don't want to waste time; in fact, they can't. That's definitely a useful service.
Almost all the other people we're talking about here are "entertainment." You can say "that's not an interview" but I don't think you get much traction with that argument. Perhaps "interrogation" is the term you want.