I am a big fan of the take-home problem. For example, Symantec once asked applicants to design a simple virus detector with wildcards (similar to grep) and then they gave interview spots to people with the best performance. During the actual interview, however, there wasn't much whiteboard coding only designing or "how would you do X" sort of questions.

I wouldn't say coding algorithms is "irrelevant". It's sort of like saying the SAT is irrelevant. It's a general aptitude test. It's not about the "relevancy" of trigonometry to your day to day work.

You could argue it's stupid and colleges should only look at personal essays and GPAs and extracurriculars. But then there's problems with that too (lack of standardization for one).

You could argue that high schools shouldn't teach trig or calc because they're largely irrelevant to most tasks in most fields and "what does that say about the system". But actually they do come into play once and awhile and lay a conceptual foundation, so they're still sort of useful to learn. And thus they form a good common foundation to test aptitude inside an hour or so, or at least no one's thought of a better one.