Now sometimes there are compromises in algorithms (I can think of 3 different nlogn sorting algorithms and I think I've forgotten a dozen more) and so the company has a propitiatory library that has an implementation with different compromises. They should have benchmarks and pros and cons written down (ad ideally be open source) so that anytime someone asks about the algorithm they can point out why they have their own and possibly contribute it to the standard library if everyone agrees to a different compromise.
These days that vast majority of the simple algorithms have already been written. I might need someone to design a more complex algorithm, but they either takes months of thought, or are just a sequence of simple algorithms.
I don't care that you really really want a solution to P = NP; you can't have it. If you try to force it, you will pay the consequences.
I don't care that you really really want a single standardized interview for what is essentially several dozen distinct positions, even if they all "use computers". You can't have it. If you try to force it, you will pay the consequences.
If you suggested that companies should have completely standardized interviews for salespeople, lawyers, and executives, all because they "talk to people", you'd be laughed at. Change it to "talking to computers" and they lose the thread.
Why not ask them real questions about the real sorts of things they're going to do, and through those see if they stuck with the problem, asked meaningful questions, etc.?
DSA problems don't bring anything to the table here, because it's trivial to substitute them with something meaningful. I'd even go so far as to say that we work bizarrely hard at asking uselessly inappropriate questions. It is easier to ask questions related to the real job.