I'm sure somebody can provide a more comprehensive history, but I'm pretty sure it started with Microsoft being cargo-culted. Then when Microsoft stopped being as cool, everybody started copying Google and how they did interviews.

Microsoft did brain teasers like "How many ping pong balls fit on a bus?" questions. Then Google copied that to start. Google later realized that performance on these questions didn't predict performance on the job and developed a more data-driven approach that you see today (leetcode style) that other companies copy today.

I'm in the camp that interviewing loops all have tradeoffs, but if you're a smaller company you can't afford to copy how big tech giants interview candidates. Their funnels are much larger, and they can afford to skip on potentially quality candidates.