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!"
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.
For leetcode, I can study once for a week or so, and then do a bunch of interviews at different companies, where each onsite is gonna take me a single day (4-5 hours or so).
For take-home projects, it usually takes way more time than that (about a whole week of a few hours every day). And it doesn't reduce the more I study or do those projects.
So no, thank you, I would rather take a single day to do a full loop with a company, as opposed to spending a week doing the same. Back when I was heavily interviewing last year, I could easily do leetcode interviews with about 1-2 companies a week without breaking a sweat. I did a take-home project a couple of times, and I am never going to do it again. The time sink on take-home projects is insane, and it is a much weaker signal. Given a lot of people here heard those stories last year where people were even trying to cheat on leetcode interviews (by asking other people to take those for them, and they eventually got caught), I imagine the cheating on take-home project is much more common and is much more difficult to detect.