And most of a lifeguard's job is sitting around blowing a whistle at troublemakers. Does that mean you'd be fine with a lifeguard who only has those two actions in his skillset? Also, as someone who has held a number of jobs that involve your 1 through 4 above: knowing basic algorithms is beneficial to the job. You don't need that knowledge often, but when you do, it has outsized benefits. Also, you wouldn't know that, unless you had that knowledge while doing that job. If you didn't have that knowledge, you wouldn't know how it would have benefited you.
The fact that "in-depth knowledge" is applied to "traversing binary trees" makes me sigh and feel uneasy.
It's more about testing the range of skills that will actually be applied. To toss in another incomplete analogy: If you're interviewing someone to build you a deck in your backyard don't spend 90% of the interview time asking him how he'd chop down trees for wood and manufacture the nails. You probably also don't need to ask him his opinion on the local building height restrictions or if he knows how to install an attic fan. You want to know that he can build a deck.
I think a lot of the above analogy mismatch and "not strictly necessary"-ness is because an application slowdown is much less severe than a drowning death. But if you account for that difference, it is very apt.
If you're interviewing someone to build you a deck in your backyard don't spend 90% of the interview time asking him how he'd chop down trees for wood and manufacture the nails. You probably also don't need to ask him his opinion on the local building height restrictions or if he knows how to install an attic fan. You want to know that he can build a deck.
But "how he'd chop down trees for wood and manufacture the nails" isn't apt at all! As a programmer, understanding algorithms is much more like 1st principles knowledge behind understanding building materials. Your contractor needs to know the structural properties of different kinds of wood, the properties of the soil in your backyard, and some basic chemistry/engineering/physics. Otherwise, she might put the wrong materials together and invite galvanic corrosion, or use the wrong materials in the wrong context and invite premature wood rot. You'd want a carpenter to understand wood harvesting, milling, and treatment in how it effects the properties of wood. Could you get by most of the time, just knowing how to saw boards and drive nails with power equipment? Sure. But someone with the right knowledge is going to avoid the unlikely but very costly pitfall and save her customer thousands of dollars otherwise.
You want to know that he can build a deck.
On time and under budget. She's more likely to do that if she's armed beforehand with certain experience and 1st principles knowledge. All things being equal, the contractors who built decks on time and under budget had good trades instruction or otherwise had the right experience and/or 1st principles knowledge. Also, if you look at the longevity and long term structural integrity of deck projects, you will likely find such a correlation.
(Also, it would be a really good idea if your contractor had a knowledge of local building regulations concerning the deck.)