As someone administering these kind of questions regularly, the majority of interviewers are aware of the shortcomings. There's a kind of 'it's the worst form of interviewing except for all those other forms that have been tried' attitude prevailing. Every other method has problems that are usually worse than those associated with doing abstract problems like implementing a BST.

From what I've seen, interviewing is evolving and focusing gradually more on realistic, practically-oriented coding, and less on Leetcode-style questions, especially as people are learning to game those.