I think this is a red herring all the way. Before you think about this problem, the first thing you have to ask yourself is: "Why do we have managers"?
Let's start a thought experiment. We'll start a company with one person. What will that person do? Manage? Of course not. There is nothing to manage, because there is only one person. Instead, although they have to plan and prioritise their work, if they aren't actually spending most of their time working, then nothing will get accomplished.
What if we have 2 people? Should we make one person a manger and have the other person do the work? Of course not. The manager will have virtually nothing to do while the working person will be overwhelmed. Although you may shift some responsibilities depending on who likes to do what, or who has various skills, unless both people are working then you will have lots of problems.
At what point do we need a manager? Well, we need a manager when the communication overhead and day-to-day chores impacts development. We only need that manager when there is enough work that they will be able to spend almost all of their day doing that work.
So what will they do? Basically anything that is stopping the workers from getting their job done. If there is a problem with communication, then the manager needs to organise things so that everybody has the information they need. If there is a lack of prioritisation, then the manager needs to prioritise/plan the work. If there is conflict on the team, the manager must find ways to resolve the conflict. I'll stop here as there isn't much point enumerating all the things a manager must manage.
The point is that everything a manager does is a result of coordinating large numbers of people or disparate information sources. Their job is to coordinate, prioritise, reduce conflict and communicate so that the workers can concentrate on getting their work done. The manager is there to "take one for the team" so that the team doesn't get embroiled in drama, trivia, or complications.
Getting back to the original problem: "you'll need to put the company first, team second and your team members third". Sorry to be rude, but that's just naive. Your function is not, through force of your will, to make all the workers do what the company wants. Your job is to coordinate information and reduce conflict so that the members can be successful. Your job would not exist if you did not have team members or teams.
And as impolite as this is, I can't finish without asking managers to contemplate the following: Is there more or less drama due to your actions? Are you demanding team members organise information for you, or are you organising information for the team members? Are you resolving conflict as it occurs, or are you creating conflicts in order to get your way? Do you ask your team to jump through hoops in order to solve a political problem, or do you jump through hoops to solve political problems for your team?
As an engineering manager, you can not succeed if the team does not succeed. It is true that your team can succeed for short periods even if some team members do not succeed, but it is an unsustainable condition. If your team members are not successful, then you have failed. <- Notice the full stop.
One way to look at "why do we have managers" is the decentralized "feudal management".
Everything starts from the owner ("king") who then delegates things to managers at various levels (starting from the board and executives) who then do their thing and either manage tasks, people and processes directly or delegate them further to lower level managers.
In a decentralized approach, if you need a small task done, you can hire me, give me some resources (money, workspace, equipment, whatever), and expect some results - but mostly leave me to myself. If you want more results, that's going to take more resources - and at some point these resources go from a salary and a desk to a budget and headcount, but in a larger manner, nothing changes; you have given me resources (more of them) and need results (more of them), and you can stop worrying about the details of how these results are achieved. In this approach, the engineering manager role becomes something like a CEO/COO of a small development shop doing custom software for their customers - and the main significant difference between this shop being internal or external is the (lack of) legal contracts required.
Another theory is that middle management's only purpose is to act as a buffer between the workers and the owners. The middle manager is just a useful idiot to the owners.
Right out of the manager's playbook: "Well, you see, I'd love to give you more than a 3% raise, but, you know, budget is tight. No one is getting more than that. Most people are getting less, you should feel lucky to be getting 3%." You know he's reading from a script that he was coached to read from.
Same strategy as calling into the support line at Time Warner cable or United Airlines with a real beef. You are immediately worn down and dejected because you realize you're talking to someone with zero authority to do anything. So what do you do? Suck it up and keep working, or quit.
I think your penultimate paragraph, the one where you ask managers to ponder, basically, if they are helping the team to roll it just push it, is very important and clarifies things. Of course, the whole comment, albeit larger than average for HN, is helping to make things clear.
We don't live in an ideal world though, and I do not know if the managers who prioritize the long term goals are more successful than the ones who focus on the short term goals (and who, frankly, usually are basically self-serving). Maybe it depends on the definition of success.
Let's start a thought experiment. We'll start a company with one person. What will that person do? Manage? Of course not. There is nothing to manage, because there is only one person. Instead, although they have to plan and prioritise their work, if they aren't actually spending most of their time working, then nothing will get accomplished.
What if we have 2 people? Should we make one person a manger and have the other person do the work? Of course not. The manager will have virtually nothing to do while the working person will be overwhelmed. Although you may shift some responsibilities depending on who likes to do what, or who has various skills, unless both people are working then you will have lots of problems.
At what point do we need a manager? Well, we need a manager when the communication overhead and day-to-day chores impacts development. We only need that manager when there is enough work that they will be able to spend almost all of their day doing that work.
So what will they do? Basically anything that is stopping the workers from getting their job done. If there is a problem with communication, then the manager needs to organise things so that everybody has the information they need. If there is a lack of prioritisation, then the manager needs to prioritise/plan the work. If there is conflict on the team, the manager must find ways to resolve the conflict. I'll stop here as there isn't much point enumerating all the things a manager must manage.
The point is that everything a manager does is a result of coordinating large numbers of people or disparate information sources. Their job is to coordinate, prioritise, reduce conflict and communicate so that the workers can concentrate on getting their work done. The manager is there to "take one for the team" so that the team doesn't get embroiled in drama, trivia, or complications.
Getting back to the original problem: "you'll need to put the company first, team second and your team members third". Sorry to be rude, but that's just naive. Your function is not, through force of your will, to make all the workers do what the company wants. Your job is to coordinate information and reduce conflict so that the members can be successful. Your job would not exist if you did not have team members or teams.
And as impolite as this is, I can't finish without asking managers to contemplate the following: Is there more or less drama due to your actions? Are you demanding team members organise information for you, or are you organising information for the team members? Are you resolving conflict as it occurs, or are you creating conflicts in order to get your way? Do you ask your team to jump through hoops in order to solve a political problem, or do you jump through hoops to solve political problems for your team?
As an engineering manager, you can not succeed if the team does not succeed. It is true that your team can succeed for short periods even if some team members do not succeed, but it is an unsustainable condition. If your team members are not successful, then you have failed. <- Notice the full stop.