Do you really need to know the algorithm?

Solving that kind of interview questions is something I always struggle with. I understand they are trying to see if you, as a candidate, can tackle complex problems. The problem is that the way they force you to solve them is not realistic.
I'd say that aside from the context of the interview, a developer should be able to solve algorithm-related problems, because that'll help them face harder problems down the road. It doesn't matter really if you're a front-end or back-end, or data architect or whatever, these types of problems should be something you can tackle.

That's my take on it anyways.

Probably stepping into a minefield, but here goes ;-)

Yes and no. Knowing algorithms (and design patterns, for that matter) and how they're put together inform how you approach problems you'll encounter as a developer.

Most of the time there's not much cause to create your own sort, search, etc. from scratch -- we all tend to reach for a library -- so it is possible to get by without them.

But if something with the library isn't working the way you think it should, you won't understand the fundamental concepts that would help you to solve the issue.

Put it like this: Learning will only make you better. Algorithms are no exception.

As an aside: Keep in mind that there's no one who knows every algorithm. I think we all encounter a few basic ones then tend to drill down into others that we encounter, have a specific need for, or just find enjoyable.