> Not a need that comes up in actual software development.
I'm not sure. Ability to remain calm and code when shit's on fire can be fairly useful skill at some places (the smaller the company, the more valuable it can be). I've did that, coding emergency patches - e.g. to cache some hot paths when we've got unusual traffic that revealed bottlenecks that we've never hit (and noticed) before. Though I'd say it's a fairly different mental experience than coding at an interview.
Also, actually writing code on a whiteboard is a weird skill outside of academic roles. But most places I've seen asked to sketch some crude pseudocode or - better - draw wavy lines and boxes that represent processes and entities, then talk about it (and I think this is fine, whiteboard here is just a convenient tool).
And, of course, requiring to remember some algorithms from memory is a rarely useful skill. I've coded even in quite spartan conditions (right in a server room, with an ancient CRT monitor and keyboard, plain vim running on a 80x25 text console) but even then I had one or two Internet-connected devices that I could've used to look things up. If a candidate is allowed (or, better, even encouraged) to search for anything they want - it's all good, of course.
Outside of education, no one bothers to remember actual algorithms unless they've used them recently - everyone remembers names and key properties, and optionally remember some core principles (and then either just use them because they're already in a library or popular package, or go look for the implementation details).