My current company favors consensus over correctness. They don't realize they do this, but they do, largely because most of the decision makers deal with subjective things, where you can spend hours bikeshedding. When they then hear disagreement on objective things, technical things, they want agreement, and view arguments over technical things as being disagreeable.
As a manager I could take that value, consensus > correctness...but I choose not to. Instead, I create an environment where my team instead chooses correctness > consensus, hashing it out internally, hidden from the rest of the company (thereby specifically eschewing 'transparency' as a value, even though it is both one we value internally, and one the business claims is a corporate value), reaching out for more information as needed but not venturing or asking an opinion until we come up with the 'one true decision' that we will pitch to them, saying it has everyone on the team's backing. At that point, the pressure to achieve consensus usually leads to all the stakeholders agreeing, too.
This is, obviously, not ideal (to where I'm looking for a job elsewhere), but it's the best I could come up with given the realities of the values the business has taken hold of. But my team's values, both their declaration and their interpretation, are not the company's values.
Real values are often unconscious, generated by the unconscious goals of the leaders.
This is not always a bad thing. Someone who has their shit together as a person can be a very effective and inspiring leader, and can even minimise the effects of dysfunction elsewhere in an org.
But any suggestion that you can have a "My/Our values are..." meeting or brainstorming session, and make it happen just by stating it and/or writing it down, is wildly naive and unrealistic.
Consciously deciding on values gives you something to point to, however. You say it's wildly naive and unrealistic, and if you mean the act of writing them down is sufficient I agree; the point being made is that defining a team's goals is -necessary- (but not in and of itself sufficient).
Without making it a point to say "This is what we want to achieve", you arm yourself, your team, etc, with nothing to actually bring about the values you want to see upheld. Sure, you can just try to do them yourselves, but is the team in alignment? Do they agree with them? When you deviate, will they call you out on it? When they deviate, will you have the rest of the team's backing to bring things back into line?
The answer is no, if you haven't stated them explicitly and gotten buy in. The answer is possibly yes if you have. It still takes effort, mindfulness, etc, but it moves from the impossible to the possible by taking the time to define them with your team.
Sure, it's possible you hire so well, so perfectly, based on unstated values, that everyone is in alignment, all the time, 100%. My experience hasn't been that. I doubt most people's has.
To break into heavy metaphor, it's important to define your 'guiding star', as it were, so you can reorient the ship when someone points out you're adrift. Because without it, you not only can't tell you're adrift, you also have no idea what to reorient yourself to.
Side note, correctness is generally a virtue, but consensus can be too. Fast and wrong decisions can be better than slow and right ones, if they can be corrected.
Most such values are a sliding scale of which you prioritize, and different priorities are better in different situations. People's feelings vs transparency, for instance. Both are important, but where exactly you fall depends on a number of factors.