Coding on a whiteboard in an interview is not "broken". What is "broken" however is making the problem the candidate needs to solve "hard". I can't stress this enough: a whiteboard coding test is nothing more than a negative filter. It's to filter out people who can't turn a simple idea into code as these people exist.
This is why FizzBuzz was such a simple problem.
But interviewers fall into the trap of thinking "this problem is too easy" and make it hard (eg figuring out a problem is g union-find on the spot and then implementing it) or, worse, they make it a crap shoot of whether you know the "trick" or not (eg reversing bits in O(log n) or the tortoise and the hare). This actually makes the test completely useless.
A negative filter is simply a filter whereby if you fail it, you almost certainly aren't a great hire but the reverse doesn't apply: there should be no A+ on a whiteboard coding test. It's straight pass/fail and an easy pass at that.
I realize some people have anxiety about doing this. Having helped or coached a bunch of people in the past about this, I can say that mock interviews and practice help the vast majority of these people. Some may be helped by doing this on a laptop in a shared doc instead, which is fine.
A few will struggle with the anxiety of that, even with coaching and practice. While I feel bad for those people, I do wonder if a reasonable-sized organization, which will generally require a certain level of communication skills and presentation ability, is the right place for you.