All of your points are sound. But notice what's not on your list: generating new ideas, the ostensible goal of many brainstorming sessions.

From what I've read elsewhere, the "alternative suggestion" that you asked for is actually a two step process:

(1) Everyone, working alone, comes up with as many new ideas as they can, writing them down. It's best if you write down some crazy ones too.

(2) Everyone comes together to discuss all the ideas on all the lists, in a more classic brainstorming format. Here is where your points apply.

The reason for doing it this way is that people universally self censor in groups, often without knowing it, and don't contribute ideas that are too far outside the previous consensus. By taking off the immediate social pressure during ideation, you get a wider range of ideas that is more likely to contain useful new ones.

Edit: I'd forgotten where I got this, until another comment mentioned Quiet by Susan Cain.