Why do companies focus on problem-solving?

I think it is important to understand why companies do their interviews the way they do them. So, the fact is that the big tech companies need to hire a lot of candidates. They also interview and hire globally. Their candidates and interviewers have very varied experience and knowledge. Therefore there is a need for a standardized interview process. The best that the industry has found is testing for coding skills and problem-solving ability. They believe that if the new hires are able to solve problems, they can learn and do anything. In my opinion, smaller and mid-sized companies should hire differently. However, most of them seem to be copying their big counterparts.