I have changed my mind about a dozen times with how I feel about the whiteboard problems for interviews, and I am somewhat on the side of "they're not good", largely for the reasons that you mentioned; it's not hard to find online tutorials to practice specifically for these kinds of problems, which doesn't necessarily correlate with a good worker. I mean, hell, I took advantage of this very feature when I started out; until very recently I was a college dropout who bought a few books on data structures and algorithms, and managed to find engineering work relatively quickly because I knew enough to do well in whiteboard interviews.

I know several engineers who are several times smarter than me, who could build basically any application asked of them, who always have trouble finding work because they don't do well with these whiteboard problems. Of course they could study and learn to get good at these problems, but at that point, what exactly are we testing?

I also think these problems are kind of bad for the other direction. When I interviewed at Apple, they gave me typical big-O notation whiteboard problems, I did well enough on them, got an offer, and accepted the job. I just assumed that if they're asking me hard CS theory problems, then there will be a lot of CS theory work at my position there. I was completely wrong about that; the job ended up being extremely bureaucratic and I spent substantially more time replying to emails and attending meetings than I ever did coding, let alone solving interesting problems [1]. I managed to hang on for about two years, but after a certain point I felt that I had had enough and left, and I always felt that I wouldn't have wasted my time if the interview process had more-accurately reflected the actual work I ended up doing.

[1] I think I had a particularly bad experience at Apple, I think other people working there have enjoyed it substantially more than I did. I think it's highly dependent on the team you're on.