At a certain point, your resume should speak for itself. The fact that experienced engineers with impressive resumes are put through these types of interviews is insulting and frustrating to the interviewees. Succeeding at these whiteboard questions requires weeks of preparation. You need to practice, practice, practice. After enough practice, you are pretty likely to pass. So ultimately, it is more of a test of "how…
One of the challenges with Google's interview process [0] is they are very worried about hiring mistakes, and also know that the process is very noisy. As such, they interview a tremendous amount of people for hiring. In addition, they've found it more efficient to just keep a high bar (missing many good hires to keep out 1 bad hire) than to conduct more than 5 interviews.
The one thing I've wonder is - if they want the top 100 computer scientists in the world to work for them, will this process produce that? Or is there another process for them?
I think the most effective way to get a job there is to build a small company and get acquihired.
[0] I don't work at Google, but I've researched the process in anticipation of an interview.