I unfortunately recognize several of these as being true from my five years at BigCo. Is this advice true of a (tiny) startup as well? Work should speak for itself when the survival of a company depends on it, right? I'd like to know if it's the same on the other side.
The larger a company is, the higher its inertia. The more sales-heavy a company is, the longer it can stay alive by bullshitting. Both of these factors mean increased decoupling between doing the work and survival of the company. And if a company is large enough that it has multiple complex streams of revenue, inefficiencies in some parts get hidden by the overall success.
I've only worked at tiny startups; I would say in the majority of cases, work speaks for itself. One thing to consider though, if you're producing good code... why would you be promoted to a position of mostly managing others? The company would no longer benefit from you as an IC. At tiny startups, even the CTO is spending a lot of time coding.
You can only code so much as you can - your output is limited to your skill, ability to learn, work ethic or determination, and time. There are all kinds of things that can waste your time - programming something that wasn’t required, programming something in a way that becomes a problem later on, oversights and other mistakes, but hopefully with experience you waste less of your own time by learning from all these previous less than optimal decisions. Now if there is more work to do than you personally want to do - it would just consume your life - maybe it is time to get some help, and then you are managing your helper in some way by guiding what they work on to help you out in the way that helps you get more work done than you could have by yourself. And then you get another helper, and another, and soon enough the team of programmers you are managing can produce more than you could have ever done by yourself. You don’t write much code anymore but You help your team solve problems with the building blocks you have, and keep them on the right path when customers and other forces will try to benefit themselves at your teams expense.
