Algorithms are just more tools to solve real world problems. Algorithm questions might be better if they were geared toward application rather than implementation.

This was a huge realization that I recently had. I didn't study CS in school, so the past couple months I've decided that I should learn the fundamentals in hopes of becoming a better developer. Learning about data structures and algorithms has definitely changed the way that I look at the world. It's nice to have knowledge of different types of problems and how to find solutions to them. Just a couple of hours ago I used a greedy algorithm to choose how to best structure my study time over the next week.

You usually don't need to re-implement an algorithm.

But very often you have to understand which algorithm to choose. Then you can pick an existing implementation.

In interviews I conduct I gladly allow to read the wikipedia page with a reference implementation (say, for the mentioned Dijkstra algorithm), or pick an implementation from a standard library of a language (say, for a priority queue). What I'm looking for is a conscious and reasonable choice of an approach, and understanding its trade-offs.

That's great! The interviews you conduct are atypical because allowing open book is most definitely not the norm for the format that forces candidates to Leetcode in order to practice.