I've been through a CS education track, including algorithms and complexity, my day job has been software development for over 5 years since I've graduated college. In practice I have been able to understand complexity tradeoffs when selecting approaches and building implementations and have been able to recognize shortcomings in the same done by others and been able to improve upon what was built. The difficulty I have encountered has never been in the implementation of an algorithm. I have even taught the first principles of complexity to others sufficiently well that I have seen them make informed design decisions.
I will openly admit that not once, during all of that time, have I ever been able to whiteboard an optimally efficient (or nearly so) algorithm implementation _and be confident it was such_. Mind you, I'd love to be able to, and I'm definitely not arguing that understanding complexity isn't useful knowledge. However I would contend that being able to bang out a optimal b-tree implementation from memory on-demand isn't first principles knowledge, but is merely _trivia_ ability.
I would further argue it's not even first principles knowledge that is most important, but rather a combination of critical-thinking, enough self-awareness to notice when you've exceeded your current knowledge/experience, and sufficient humility to fix that lack rather than plod along with blinders on.
Granted, I might be less competent than I believe, but then, in practice, it would seem that incompetence can lead to genuine success. Perhaps the scope of my 5 years real-world experience is so narrow that I've simply not had the chance to encounter a situation where others would say "if you're not able to whiteboard a b-tree, you're not the right person to solve this problem". But then, I'm a full-stack developer that regularly uses Java, Javascript, and Python and have occasionally had reason to use R and C#, so it seems unlikely that my experience is that exceedingly narrow.
Sorry that this became a bit rambling, it's just a topic that's always intrigued me in how divisive it can be.
a) What the heck is an optimal B-Tree? (Don't you have to tune the parameters? b) I would also contend that it's trivia, and merely a way of getting at the ability to apply First Principles knowledge.
I would further argue it's not even first principles knowledge that is most important, but rather a combination of critical-thinking, enough self-awareness to notice when you've exceeded your current knowledge/experience, and sufficient humility to fix that lack rather than plod along with blinders on.
So you're not disagreeing with the value of 1st principles knowledge. Then you cite an even deeper kind of knowledge. Where exactly are we disagreeing here?
Usually I don't bother engaging in arguments with these people because I know that the standard algorithms interviews will weed these people out so that I never have to deal with them but I've started to notice a trend in more of these people finding their way into the "big 4" type companies and ending up on large scale/infrastructure projects where they end up making very critical mistakes, see https://news.ycombinator.com/item?id=13700452
But the op is basically implying that you don't even need the "cocktail party level familiarity." Knowing just enough first principles chemistry to know how CO2 and CO are produced can save your life. It's one thing to just know the rule you shouldn't run your car in a closed garage. It's another thing to know the general conditions where you might be producing CO, so you also know not to run your laser cutter in a poorly ventilated room.
First principles knowledge are a series of tools for reasoning about the world, your program, your software libraries, etc. Programmers thinking they don't need to know the most basic algorithm knowledge is basically the anti-intellectual stance of eschewing first principles knowledge.