I'll have to disagree. Your justification of why do puzzles:
"Finding people that can work together effectively at scale"
has no connection to these challenges whatsoever.
If this was the priority thing that "big companies" wanted to optimize for, then testing would be focused on a potential managers ability to prioritize and coordinate tasks and/or on an employees ability to follow directions and seek clarification when there is ambiguity.
Neither of these things is tested with "brainteasers and algorithmic puzzles". What these things do is make the puzzle master feel smart (typically at the expense of the puzzle taker) and will weed out thoughtful and less self assured candidates.
In short, you optimize for the classic "brogrammer". If that is what you seek and is the culture you want to cultivate, then great. Keep doing your interviews with brainteasers.
From my personal experience, I was being second round interviewed for a senior position and the interviewer asked me two questions.
1) While at lunch I left one of the lights in the conference room on and turned the others off. Which light did I leave on?
2) How many tennis balls fit in a tractor trailer?
After the second question, I stopped them and told them this was not the kind of environment I was interested in working in and left.
