I don't get the product manager hiring process

I started as a technical project manager over 10 years ago and slowly moved into product management in my last job almost 5 years ago. Cannot say it is a very successful product (due to the technology and market choices, both made without me at the very early stage of the product). But the reason I'm writing this post is to say I don't get the hiring process for product managers. And before I go ahead, I accept that the problem can be with me and not the process. But the process feels entirely superficial and arbitrary to me. The typical problem given at the interview is like 'Design a solution to the problem X'. What exactly to do next is an entirely subjective choice. I've read the famous "Decode and Conquer", but even then it leaves a lot to be answered. In the end you are not really solving the problem, you need to please the interviewer instead. Do they want you to challenge the problem first? Do they want you to challenge the suggested technolog