"I want to work for your company"
"Ok, prove yourself"
"Sorry, I don't have time"
How do you expect that conversation to go from there? If you don't have time then make time. It isn't anyone's problem but your own.
Loonnnng time ago (25+ years) I remember appearing for an entrance exam of a very famous, hard statistical course. It was a 3 hour exam, with only 7 or 8 questions. The exam explicitly stated that they do not care much for the actual answer, but the path taken to get to the answer (all questions were math problems). As a kid this sounded weird to me, but now it makes sense. Someone with good problem solving instincts will get to the right solution (even if it takes a couple of attempts to get there) vs someone who got lucky the first time (or brute forced their way)
Pretend I was hiring a restaurant chef and the industry standard test was "run a mile in 4 minutes", a test that 98% of all candidates fail!
So professional chefs practice by jogging daily so they could prove themselves during the famous "run a 4 minute mile" weeding test so they can be hired to prepare meals for people.
That's what we're talking about here. I've had to write out the mathematical proof of various algo complexities of B* trees exactly 0 times when writing SDKs for some CRUD application but that's what's expected during the interview.
It's as correlated with the ability to do the job about as much as running a 4 minute mile in that younger, more desperate, easier to control, and thus cheaper people can do it better. That's what the actual filter is for - to find candidates that are easier to abuse and take advantage of - smart enough to do the work and foolish enough to take the job.
I've hired large teams at multiple companies where such tests were used and that was exactly why we did it. We didn't want the experienced 45 year old wanting to work 40 hours with vacation, we wanted the foolish 25 year old that gave us their weekend.
Actually saying that is illegal, but using a stupid test that selects for it is not.
"But this isn't relevant to my job, a subordinate will always do this kind of stuff."
"We are a fine dining dinner restaurant, I'll never need to make an omelette."
Doesn't matter, make a damn omelette. If you can't, you aren't suited to be a head chef, or any other kind of chef.
Knowing basic data structures and algorithms and having problem solving skills is absolutely critical to a software engineering job. In fact it is the entire job.