People tend to forget the historical context of a policy. Google was small in the early 2000s, but it was one of the hottest companies in the valley. Therefore, it could afford being picky. It was solving really tough computer science problems in massive scale, so it needed to find talented true geeks, those who live and breath math, engineering and computer science. The so-called brainteasers were usually thinly disguised and well-designed math or algorithm questions. There were few interview-prep books back then, either. Therefore, those who could solve the teasers were likely creative geeks.

Fast forward to it today, we have huge amount of prep materials and prep schools, so it becomes hard to tell who's truly talent and who has great memory. Google doubled its workforce in the past three years from 35,000 people or so to 70,000 people. You just can't expect that everyone is passionate and talented about math or engineering. Besides, Google does not need too many of this kind of people either.

However, if a small company is tackling a hard problem that does require tons of math, computer science, or pure ingenuity. Hell ya, brainteasers can be of great help. They don't even need brainteasers, they can just directly ask math problems.