After a grueling interview process at Goldman Sachs, with 7+ technical interviews that required me to solve very specific questions on college-level Maths, Stats and Computer Science (admittedly, I was applying for a quant job position), I was eventually asked to interview candidates myself. While I did not feel entitled to change the current interviewing culture at the company by asking questions of a completely different nature from what I got asked in the first place, I conducted my interviews in a very similar way to what you described. By no means did I expect applicants to reach a definitive answer, but I instead worked on the problems with them to see how far their intelligence, creativity, curiosity and, most importantly, their ability to well communicate their thought process would take them.
Such interviews used to take a while hour of my time (which is a lot to afford when you work in a bank), but by the end of each I believed to confidently ascertain the candidate’s ability to thrive on our team. In retrospect, it has served me really well.
All in all, the problems posed (and the solutions given to them) might not carry as much weight in the final decision as the discussion held with the applicants. As long as the questions asked give them some material to work on, and DS and algorithms usually serve this purpose very well for us engineers and developers in general, one should be able to effectively select candidates given some time investment.