Politics does not have to be a zero sum game but often those who view it that way and are absolutely ruthless rise to the top. Perhaps that's just the human condition.
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.
It's a mistake to think that it's not a zero sum game.
If there are 5 people and one available spot for promotion, you can get selected by bolstering your appearance or by tearing the other 4 down. Either one works.
And yeah, the best tactic is usually "make my boss look good".
You say this like it's a bad thing. You should be making your boss, your team, and your teammates look good. If you are doing those things, you are probably also making the company look good.
It's thinking about the long vs. short term. Focusing only on your own optics may work okay in the short term, but they cap out fairly quickly.
Think about how it looks from the outside. Employee A is only focused on themselves. It is recognized that A is good, but any team A is on still struggles. Employee B makes the whole team look good. It becomes recognized that B not only does well, but any team B ends up on does well. Who do you think advances the farthest long term?
I certainly don't think it's a bad thing to make your teammates look good, but in general it's more effective to give the lion's share of the credit to the boss rather than them. And credit is a limited resource.
I say that like it's a bad thing because it kind of is.
I believe there are some companies where coworkers rather than management decide promotions and this tactic would not work but they are few and far between.
This also has nothing to do with a just world fallacy. This is thinking long term. Rarely can someone politic all the way to the top. In order to lead, you need the support of your team. You get that by being a great team member yourself.
/rant
Finally, I'm tired of hearing how awesome people are, but their team sucks or their boss sucks (doubly so for people working at FAANG, because the low bar is so much higher). If they are so awesome, then get out there and help the team improve. Instead it's I'm so smart, but everyone is holding me back. I'm stuck on a crappy team, etc... Grow up.
/rant over
If you want to succeed as a SWE at a FAANG company you'll have to be an exceptional engineer, or have other skills (leadership, pm, ...). You can't just weasle up the ladder by playing "political games".
Though, most of my colleagues don't even care about their career - most of us just want to work on cool projects which immediately affect billions of people.
I worked at one the FAANG and I found in my team and some of the neighboring teams the most insecure, unfriendly, back-stabbing, conspiratorial bunch of technically semi-competent losers I ever had the displeasure of working with. Other people were competent, trustworthy, confident in themselves and thus enjoyable.
I also interviewed at other FAANGs and maybe the interviewers were all wonderful people, but I had a mixed experience. Some appeared to be ok, some definitely not. Very different experience from the parent's.
I think a lot of people would enjoy a blog post elaborating on that experience (possibly under a pseudonym to protect you from vengeance).
Wonder what the false negative rate is?
Google's culture and hiring process is so well documented at this point, I suspect any suitably talented individual could appropriate some cultural fit.
Of the (current and former) googlers I know personally, they are a mixed bag but there are some traits that are more common. Self assurance and the uncanny ability to never be seen to be demonstrably incorrect are prevalent tbh - but that applies equally to most of the industry.
I think that may be very easy to do, just state that everything you say is just a theory or your opinion... but this is just a theory.