1) one or two people in the discussion (interviewers) already know the perfect solution to the problem and are contributing as little as possible to the discussion.
2) the actual amount of allotted time to brainstorm a solution to the problem is realistically only ~10 minutes not the ~45 minutes you are allotted because of the time it takes to implement the solution with real code.
It would be nice if no one in the interview knew the answer to the problem before starting the discussion and this discussion would be pretty realistic aside from the lack of help from the interviewers. However, you cannot easily/fairly compare candidates with so many different questions.
Technical interviews would also be far more realistic if they allotted more time for problem solving but I imagine if the standard 45 minutes was bumped to over an hour, the only outcome is that more candidates would perform very well and that's not an outcome companies actually want unfortunately.
My personal opinion is that all of this should be scrapped in favor of seeing what the person has produced and having them partially implement a solution of something they have written in the past. It is a virtual impossibility that anyone could work on a project of any sort without being able to sit down for an 8 hour interview where they are responsible for partially re-creating something they have worked on in the past. To this day I still remember large parts of source code I've worked on 10 years in the past.
Why would this be the case--at places where the number of candidates far exceed positions? This is the exception rather than the common case.
Even the very best tech companies are constantly filtering through thousands of people who claim to have worked on extremely complicated development projects but can't code extremely simple things.