Being a senior engineer means having confronted a shitload of different minutia type problems from network stuff, compiler bugs, language nuances, threading nuances, etc. and having spent time figuring each one out. Not that senior engineers can reiterate all that minutia off the top of their head, but it gives them a good intuition for how to solve problems when they hit them making them significantly more productive than junior devs that have to figure them out from scratch.
I don't understand what's so hard about this, testing algorithmic knowledge tests if the individual studies and implements algorithms. It's very simple. And yes, people have stress reactions in test type settings (I don't for paper tests in school but apparently I do for live coding mostly because I don't know how to implement different algs).
Stress during interviews is insane. Once I was at the tail end of solving an interview problem but it came down to multiplying 9 * 3 and my brain wouldn't fucking do it (apparently I can't fucking multiply).