A common example brought up here on HN is binary search. It is usually simple to figure out that a problem requires Binary search and even which variant. But the differences between the variant are really small and you can very easily make a mistake when implementing it.
I have passed enough of these interviews myself and used to think similarly (all you need to do is learn the fundamentals and the rest will follow) but my hit rate went up substantially when I realized that I had to do the same problem again and again and it almost became part of my muscle memory. Looking at a new problem, analyzing it and then coming up with a novel solution takes a lot of time, and there are several mistakes you can make on the way. The interviewing culture today is to reject "false positives" so anything apart from a perfectly coded response results in a mixed/negative response.
This whole leetcode thing is a farce and has to end. Let's be honest, the Google guys used it because they wanted "like-minded people". In short, they discriminated based on their own criteria and successfully brushed it off as a "fair and unbiased" way of selecting people.
A take home test requires spending free time for everyone. A whiteboard interview requires variable amounts of free time. I would wager that, on average, the people inside companies using these processes require less time to "grind leetcode" than the people outside those companies do.
You gotta be able to convince the folks on the inside, not the ones on the outside. To them, it being hard to "grind" might even seem like a good thing! "It's hard to cram for this compared to other sorts of tests!"