Ultimately in any organization power originates from a legal source and fans outward via a network of trust relationships. The structure of the network is a hierarchy, with individuals closer to the source wielding more influence. It can be explicitly codified, or left implicit as is often the case in "flat" organizations.
In either case, the best way to move up the ladder is to become trusted by people closer to the source of power. This requires social aptitude, there is no substitute.
I think the flat vs hierarchy debate is pointless. Instead the debate should be about what kinds of people should have influence in a company? What standards should be communicated to ensure that smart latecomers quickly ascend the company's social network? Values, such as obedience and conformity, tend to reinforce the social hierarchy. Values like dissent and diversity create a more fluid social environment where trust relationships can be forged across different social strata in a company.
I think this social fluidity should be emphasized over "flatness." I'd much rather work in a fluid company than a flat one where people are binned into overly formalized teams of influence. I suggest that if you want good people to rise to the top, make fluidity the DNA of your company.
The power of influence and respect can't really be formalized anyway. If people think technical excellence and the company's technical success are important to their personal success, then the best technical people will wield power through their ability to inform and advise. If your best technical people have less power in the organization than they ought to, it's because other employees intuit, probably correctly, that technical quality has nothing to do with their personal success.
The problem with hierarchy generally is not in the concept - it is in the implementation, and its poor scalability.
[Disclaimer: I herd geeks for a living. I get to call it. That does not mean I think I am better than my coders, nor that I know more than them, nor that I should be paid more. I like to think I am an asset to them].
Serious dissent between companies is good, but strong dissent within means no guiding vision or purpose.
"There is no amount of training that would make up for the talent we’d extinguish by teaching them how to write annual reviews."
Leadership has nothing to do with writing annual reviews.
I heard that leadership means gathering people's power to accomplish a goal.
So while leadership may mean management, management is not inherently leadership.
More importantly, there are leaders who aren't even _good_ at management tasks. Just because everyone trusts your opinion on architectural design doesn't mean you should be assigning tasks, or prioritizing the backlog.