>It’s a mistake, and will set you back to think of politics as a zero-sum game.
I think we have a bit of a meta-false-dichotomy here. I agree it's a mistake to think of it as a zero-sum game. I also would say it's a mistake to think your advice will reliably work.
I've often sat in career advice talks and they often give the same advice you gave. Invariably during Q/A someone will point out they followed that exact advice and got screwed. The responses by the panelist fall into two categories:
1. I don't believe it and there must be more to the story.
2. You're in a poor organization. I suggest you find a better place to work.
So yes, the advice is good, but only when it works :-)
As a company gets bigger, the likelihood of faulty incentives existing goes up. The likelihood that what's good for my team + boss is bad for the company goes up.
Personally, I don't have illusions. I've worked in jobs where the advice you gave won't work. And I side with the second answer. Instead of playing bad politics, it's just a lot better to find an organization that is worthy of me/you. The advice people who had been in the org gave me was consistently "Forget about what's good for the bigger picture and the company. Make your boss look good even if it's a bad solution and will waste others' time and money." I didn't follow that advice and I paid for it. At the same time, my time and effort is valuable - I'd rather use it for something better than this. Either I work to change the organization's culture, or I leave.