there's a post somewhere that talks about this exact thing, that (while yeah he could be less of a dick about it) he's still the one in charge who has to make those hard decisions. he's the one who has to say no, who has to be looking at the bigger picture, the ED as a whole. he does try, he looks for and tries to provide workarounds on an individual basis (calling the prison for Gus, letting Roxie [the mom with cancer] and her family stay, fudging the dates so the teen girl can get an abortion, making Langdon go to rehab instead of reporting him outright, letting Donnie leave early for his baby, etc). but sometimes, he has to be the one saying no, we can't do this, it would affect too many other variables (having to let the ICE agents stay so they can help Pranita, not wanting to let Gus be admitted, telling Baran she needs to disclose her seizures to higher-ups, etc). when they find a way to make it work, he agrees.
no one wants to be the guy saying no, but thats the job -- and it's why i agreed from the beginning that Baran has a lot to learn about doing it, that maybe Robby's right to be a little trepidatious about her ability to run the department (though again, should be way less of a dick about everything, but thats sort of a blanket disclaimer over the whole discussion). like op said, she thinks on an individual level more often than not. that's not a bad thing on it's own, a lot of them do that (Abbot especially); but when you're the one running the whole thing, you can't be as individualistic as others might want. Robby is right about the lack of open beds, about getting ICE out as quickly as possible, about Gus being a potential risk, that McKay shouldn't have been treating a patient elsewhere while she had one actively passing -- there's nuance to every situation, but ultimately he's pretty consistent about going for the best overall choice for the department as a whole, patients and staff alike.
the arguments he has with Dana over the versed and with Baran over her seizures also show the difference in thinking pretty well. Dana is charge nurse, so she also has to think about the bigger picture, the forest instead of the trees. still, she tends to allow her own biases and feelings to make some of those bigger picture decisions. she carries the versed because she was attacked, and has decided that that sort of offense is the best way to keep her people from going through the same thing. she's right that the nurses deserve better protections, that it's been made very clear that they have to defend themselves because the hospital won't. and Robby understands this! he even says "i'll sign an extra order [for versed] so you can have one when i'm gone." what he's worried about in that argument is how this could backfire -- on Dana, on himself, on the nurses. he wants to protect them legally and emotionally. it's why he's stressing about why she had the vial in the first place. it's why he told her to pass that patient off. Dana yells at him and turns it into a fight about his sabbatical, but the point still stands that while she was right to defend Emma (and herself, and her staff), the way she did it could've come back to bite her in the ass.
the fight with Baran is a very fascinating showing of how they each think, and part of the issue is that they're each mapping their own way of thinking onto the other. Baran tells him he's selfish, he's thinking about "his department" and nothing more. the verbal stressing that the department is his is very interesting to me, because it shows that when Robby says "my department", the most important part of that sentence to Baran is the ownership. that Robby's worried about what's his (the ED) and not what's her's (the seizures). in her eyes, she trusts him with what's her's and he doesn't do the same in return because he thinks he's the only one who can be trusted with it.
Robby, on the other hand, is thinking about how her disorder could affect the entire department. she's had sudden episodes twice in one day, both times over patients. the treatments she may need would cause her to be out of work, meaning a staffing shortage. the seizures could happen while she's actively working on a trauma patient, causing further injury or even death -- which could then trigger a lawsuit against her and the hospital for allowing her to work while impaired. her condition could worsen, she could develop new symptoms that would make it difficult for her to do both the physical doctoring and the administrative-ing that being (temporary) chief comes with. her teaching could be impacted. and personally, it could (and does!) take a real genuine toll on both her physical and mental health. her skills as a doctor aren't ever called into question, even before he sees them. it's the ability to run the department that he's concerned about, because if the chief can't run the department, the department falls apart. he thinks she's ignoring all that when she decides not to tell anyone else, which is what pisses him off.
(obligatory the fight was also at the end of a 15hr holiday shift from hell and Robby is in fact being a dick on purpose for suicide reasons)
that line of thinking isn't all good, obviously. it's why he's so harsh on himself (and Samira) when he breaks down -- if he can't keep himself together, it's going to have major affects on everyone who depends on him, patient and staff alike. he can't break, he has to be there, he has to be On, he has to be "the bee protecting the hive". it's what makes him a good leader, and it's what's killing him.
(i could -- and maybe will one day -- do another whole thing about Robby and Samira because it's so vibrantly glaringly obvious that he's terrified she'll become like him, and also that most of the more egregious moments of him being a dick in s2 were all Robby trying to make sure that their mentor's (his own) death wouldn't tear them apart like Adamson's did to him, and it's easiest if they hate him and remember him as an asshole. not on this post though lol i'll make my own)
anyway this show's got great character work, it's absolutely just made for this kind of discussion and analysis michael robinavitch they could never make me hate you