I think we are completely in agreement about what constitutes skill, and what companies should look for in candidates.
The point where I think we disagree, and please correct me if I'm wrong, is: are LC style questions an effective testing method for these skills.
I say no, they are not, for 2 reasons:
a) implementing something like a non-trivial graph algorithm doesn't come up often in day-2-day work, and if it comes up, even some experienced developers look it up, just to make sure they got it right from memory. To borrow your dishwasher-analogy: I want the repairmen to know how a generalized dishwasher works, so he can repair Miele, Bosch, whathaveyou, but I don't need him to be able to program the DWs microcontroller on a whiteboard, or forge one of the pipes with nothing but a firepit, a hammer, anvil, crucible and some copper-scrap.
b) since all these questions are known problems, both in their solution AND their usage as test questions, we are facing a "learning for the test" dilemma: people can, and many do, just memorize these answers to pass interviews, same as many students in standardized test environments just learn how to pass the tests.
This is fundamentally different from understanding the subject. Again, I agree with you: I want someone who can answer these questions because he can apply generalized knowledge about algos and data-structures.
But I am not confident tests which rely on pre-fabricated and well known puzzles will give me that.