Yes there has been an episode where the brothers don't appear together (nor are they working together).
And while yes the episodes do devote some time each episode to show the brothers reactions to the events of their lives or the behavior of the other. Thats realistic. Every day you experience events that remind you about your past and current problems. You react, be in just a look, or a change in tone. Your at work and a coworker talks about something that makes you think of your own experiences (be it better or worse) you react to that. Each and everyone of us does throughout or waking life.
Now you might not want to watch that in a show (and I can understand that). But that doesn't mean character's wouldn't legitimately experience it. In fact the show doesn't even come close to showing us how dark their lives should really be.
Look at up to this point in the first season.
Dean is clearly hurt that Sam left, yet how long did it take for Dean to even address that issue. Sure when something comes up that reminds him of that he reacts. Sometimes with humor or anger, sometimes with just a look. But actually talk about those feelings...Not damn often.
When Sam knows something is off, something is deeply wrong, does he just open up and talk to Dean about it. Nope sure doesn't. It takes the mortal threat to others to get Sam to even admit anything is up at all.
In my family experiences and the experience I have witnessed in others, thats fairly true to life. You dodge and deflect and only talk when you really have no other choice or things have gotten seriously, seriously bad. But you always react, even if its subtile in your day to day life, you always react.
That in and of itself it isn't melodramatic. That's realism.
I think that when I hear a viewer state that this show has too much angst there are two ways of taking that statement.
1. That it isn't valid for the characters to be experiencing strong emotional reactions to their environment and experiences.
2. The viewer just doesn't want to see that in their entertainment.
I can understand 2, as their are programs that are great and well crafted but don't appeal to me for weekly entertainment. But number 1, I can't as the show really doesn't focus so much on the real emotional and physical trauma these two characters would experience.