Essentially I agree with you - most of the reason is cargo culting Google.
Assessing software engineers is hard. A couple decades ago, Google (which at the time was a tech darling, and the #1 place to work) had a saying of "A players hire A players. B players hire C players". Essentially they were terrified of hiring bad people, because they figured the company would inevitably go downhill if they did. Their hiring process was essentially an expression of this idea - it was based on the philosophy of "we're all A players, but are you as clever as us?". Interviewing at google at the time involved sitting about 6 back to back whiteboard interviews with programmers. Each person would spend ~20 minutes asking you their favorite puzzles and things, and seeing how you did. Nobody can say this because it would be illegal, but it was in many ways a programming themed IQ test. Good questions were the ones which filtered candidates out. And its easy to recommend against hiring someone if they couldn't reverse a binary tree on a whiteboard in 20 minutes. (I mean, thats easy for me! They must be a C player.)
Other companies followed suit. I mean, hiring is hard. Why not just copy Google's approach? Microsoft did something similar. Facebook was full of ex-googlers, etc etc.
The problem is that being able to reverse binary trees doesn't correlate with how well you can manage a database, style a form, fix a memory leak or talk to your team. And the people who only had those useful skills are unhireable. Oops!
In my opinion, the right way to interview programmers is to make a list of skills you want your programmers to have (coding, debugging, CS knowledge, communication skills, architecture, ...) and then find ways to assess each one. For example, to assess debugging you can give your candidate some pre-prepared code with failing test cases and see how many bugs they can fix within 30 minutes or so. But that requires preparation and test calibration. Most companies struggle to convince their engineers to interview someone for 20 minutes - let alone spend a few days putting together a problem like that.
Knowledge of data structures and algorithms is useful, and it is a positive signal about a candidate. But (depending on the role) I'd weight it below communication skills, raw coding skill and debugging. Those are all much more valuable. We need to start treating them as such.