> I was a hiring manager at a big company for years. We never did coding tests, and I like to think that I made good choices every time.

I don't doubt that you did, but I doubt that everyone at your company places the same effort as you do. At my current company, 90% of interviewers half ass their interviews. They don't have much incentive to care, so you want interview questions with consistent standards and produce some signal with minimal effort. Algo questions fit this bill perfectly.