Really? I find them pretty relatable. They're professional yet familiar with each other, like the way Batou makes jokes.
Yeah, everyone in the show is so austere and uncaring. Togusa gets shot and Major and Aramaki rush in and just want the data. There's no hint of genuine concern or a 'hang in there, buddy' moment. The show in general is so wooden that any time there's humor or light-heartedness it feels awkward.