While it's true that you'd be less likely to do something drastic around others than while alone, that's not exactly what I was getting at. Being with other people, just having another or a few other heartbeats in the room, is often healing if we let it be. I disagree with the rest of your reasons. How do I know? Because I do it, too. The way I sort of work with these feelings of just being a burden to everyone around me is to look at it from the other person's side. Let's say someone in my family called me for help with a psychiatric or emotional crisis. Would I feel burdened? No, I would be honored that they trusted me, and I would love to help!
The thing is that people in general want to help one another. There are, of course, sociopaths, Narcissistic PD affected individuals, and others with a trauma history that has taught them to make sure to get what's "mine" before anyone else can take it from them. These might be a significant portion of humans when taken as a whole, but really this is much more rare than our depression wants us to imagine. Therefore, for the most part the people who I love also love me and, like myself, would not be burdened if I should need help. When I look at it this way, it's sort of like I'm denying everyone the opportunity to help if I don't reach out. At this point, I realize you have an endless array of counter-reasons, but I'm not trying to convince you. Instead I'm trying to present another perspective, because this is what has helped me start to climb out of this hell I'm in with depression.