It is okay to care, but nobody is always right, and noone has a monopoly on good ideas.
It follows then that the person who just 'cares too much' will be on the wrong side of a decision. At that point the best outcome is for them to either change their mind, or let go.
Caring obsessively can be a negative in some competitive environments, e.g., a very insular/non-collaborative university department. But I suppose I might not call those other professors coworkers.
Someone who cares obsessively about things that are closer to their coworkers area of responsibility are a liability to a team IMO.
Caring obsessively about your own responsibilities is great. It is a pain in the ass from time to time, but that pain is worth it.
While I agree with the premise, the "downstream" really matters though.
There's a lot of different ways to care obsessively and many are quite toxic if you've ever worked with them. One example comes to mind is I've been there were PR comments are way overbearing. There's definitely good points/notes, but nitpicking, snide comments, holier-than-art attitude easily comes along with the boat.
"With love" is such a blase statement, but it really has to be the starting point. That caring combined with respect has to be present to be a healthy, long term working environment.
Like with many things, there's a balance.
I find that I want different kinds of feedback through the process of developing a PR, and whether it's over a day or a month matters a lot too.
That way, I can safely be obsessive about things when giving PR feedback, in the knowledge they're asking for "debug level" feedback, or give it just-the-facts review if they're just trying to get something merged that has been reviewed to hell and back.
Consider a soup kitchen vs a supermarket checkout. The people working at the soup kitchen arguably care a lot more. The person at the supermarket checkout can be as glassy eyed as they feel and still be part of feeding more people in absolute terms.
Humans seem to have some sort of emotional heuristic to focus on care (really, focus on motivation of others I think). That works in small groups but it is highly misleading in large ones. In large groups, the only factors that matter are incentives and competence. If the incentives are good and the people are competent, good results will happen. If the reverse, corruption. The motivation heuristic actually does a lot of harm because it causes a huge amount of noise in the discourse where people whinge about this person or that having bad character to no avail. It is often true that people have impure motivations, but at scale that is true of effectively everyone. There are the devils you know and the devils waiting to become known. We can get great outcomes regardless; our politicians are cut from the same cloth as the Nazi and Communist parties but look at the difference in outcomes.
One of the most peaceful insights I ever stumbled across was that of the people in the workplace who cared less than me, there were a significant and productive subset who were just doing more good than me through competence and being thoughtful about what work to pick up.
It's closer to a craftmanship kind of care. Being proud of what you're putting into the world. Caring that it works well, not because the purpose is important, but because it's something you're doing and you want to do it well.
But it is management's job to decide on software quality standards and provide feedback to devs. Expecting the developers to be responsible for quality as a baseline is just a path to burnout for those devs; because then they are going to go mad because everyone on the team has different personal standards. The person with the highest standards on the team will never be satisfied.
You can't reasonably expect teammates to cover for bad managers, it is much cleverer to learn to identify good managers and try to work for them. Or become one.
To me, caring means expecting work to be done to your standards instead of an independent standard.