The best interviews I've experienced, both as an interviewer and an interviewee, are the ones that feel like two team members collaborating to narrow down requirements and solve a problem.
> about the algorithm or the promise of a particular solution
It's not about "the" algorithm or "a" solution. It's about you the candidate being able to propose multiple solutions, perhaps with space-time tradeoffs, to provide a recommendation based on your judgement, and to ask the interviewer what they think of your proposal.
My first round I passed with a less than optimally efficient solution, but he was satisfied every step of the way during my work.
While I was lukewarm to the prospect of working for Facebook, the interview process was very positive and reflected very well.
On a personal level, self interest would have me like the leetcode style problems because I can get most of them right on the first try during a timed interview, without studying. If I were pursuing a job at a FAANG, I might actually study them and I'm sure it would go well for the testing portion of the interview.
However, when I interview this is not what I'm looking for. I'm typically looking for someone who knows the particular language that I'm hiring for. My questions run from the very simple to as deep as they can go on either language or implementation details. From the most junior to the most senior, they get the same starting questions and I expect the senior people to go deeper and explain why they choose something over something else. I'm also testing their ability to explain it to me (not just get it right) as that is part of their job working with juniors.
I really don't even care if they have the names of things right and don't really count things wrong against them if they get the names of two things backwards for instance. For example in Go, a huge percent of the time you might use slice over arrays. Some people get the names backwards, but can identify which one they actually use and they know that one can change size. They are correct in usage and misnaming them. I inform them of the name, encourage them a bit and move on.
I've never liked the "look at this code, what's wrong with it" approach. There are too many contexts that I have to jump into at the same time. There is often an expectation that I find a specific problem with it. I'm lacking the usual tools like an IDE or compiler. What level am I looking at in the code? Does it compile? Are there off by one errors? Cache invalidation? Spelling errors? Logic errors? Business errors?
This guy has missing tests on code that needs to be refactored in order to make those tests. Maybe he has it figured out just right, but the "jump into my code" interviews I've been in on all seemed like they had secret gotchas that the interviewer expected specific answers about.
In short, I haven't seen a proper, repeatable process for interviewing for software development.
The interview for my current job had something simpler: something like finding random permutations, then what's the algorithmic complexity of this random algorithm. (It was years ago, I forget the details of it.) I just talked through the solution. That was nicer that having to come up with questions. :)