Oh, good grief. Being able to answer basic algorithmic questions in an interview isn't a high bar, folks. It's not as if a basic tree-traversal question is going to trip up everyone but Don Knuth.

The biggest danger you have as an interviewer is allowing a Stealth Incompetent on your team. These folks all have Github profiles, points on Stackoverflow, fancy blogs, webpages, etc. They might even have nice-looking, public-facing projects. You can even argue that these people Get Things Done (for some value of "things"). But they're still bad hires.

Stealth Incompetent programmers are great at using other people's code. They can install gems, download jQuery libraries, and stick them all together. They can make websites with Rails or Django or some other framework, and know enough to be able to piece together functional "products" from parts. All fine. But unlike actual engineers, Stealth Incompetents fall on their face the first time you ask them to do anything that requires taste or independent thought. They're the people who will introduce a horrible dependency on a bad gem, or architect a solution that takes quadratic time, when they could have trivially done better with a tiny bit of thought.

Algorithmic questions are designed to catch incompetent people before they can infiltrate your team. The "relevancy" of the questions to the day-to-day work is immaterial.