I got to about page 5 before I decided I knew how this thread was progressing.
In short, you have too much faith in people, while at the same time dismissing the flaws of your idea. This is basically, a horrible idea. I'm going to try talking this on a point by point basis.
Firstly, BSN is a very small portion of the community, and the group within it that really understands the game balance is even smaller still. You are giving a great amount of power to a very small amount of people. You claim that "the people that really care about the game are already on BSN" and that "if they want to vote they can just join BSN and vote". Both of these are elitist and ignorant statements. You basically claim that the only people that matter are on BSN, and if anyone takes offense to that they should just join BSN.
How are people not on BSN supposed to know that there are even balance changes being done on BSN, or even to go so far as that BSN exists. The obvious answer one would give is to "put up a notice to go to BSN in-game". How often will this notice come up? Once? What if it is accidentally skipped on habit. What if someone decides to check it out later because they actually wanted to play the game when they started the game and forget the web address. Can you find that information again later if you need to? What happens when BSN account policies confuse or deter people and they end up giving up on trying to use BSN? Do these people not matter because "they didn't put in the effort to join"? Should we be invaliding the opinions of people based on such frivolous standards?
You claim that bioware doesn't need to test this because the community can test it. How do we "test" non-existant number changes? PC players can mod their game and see first hand what these changes will be like, but what about Xbox players, and PS3 players, and that Nintendo thing people forget about.. We can't see how these changes will actually affect gameplay. PC players are a very small percentage compared to the console playerbase. Should the balance of the game be completely differed to PC players with the tools to do actual empirical testing? The PC players with framerate adjustments, modified FoV, a entirely different control scheme, and a dedicated reload cancel button? What about the people that don't care about any testing and just make their choices off gut feelings? What happens when people feel that the Suppressor is too weak because they didn't do well with it, when they just didn't know how to use the weapon and went for body shots? Should people without extensive knowledge of gameplay not be given an equal vote because of their ignorance? Does that not defeat the entire purpose of opening balance changes to the community?
What level of play are we balancing for? Many of the very active people on BSN play a majority of Gold or higher. Most opinions on gameplay will be coming from their in-game experiences, which will be of level on gold or higher. The most recent estimate I can recall placed around 80% of the playerbase in Bronze and Silver. If the game is balance around higher difficulties, what happens to lower ones? What keeps the hard difficulties hard? You commented earlier by saying that you felt that bronze was the "intro" difficulty, silver was easy, gold was normal, and platinum was hard, but that is completely wrong because platinum didn't exist for a large amount of the game's lifetime. It started as just Bronze, Silver, and Gold, respectively easy, normal, and hard. When people complained that the hard difficulty wasn't hard enough, the made a super hard difficulty, which created the illusion of difficulty by differences in scale rather than differences in kind. The game was continuously balanced around the "normal" difficulty, Silver, because that's what made the hard difficulties hard. I have a feeling you'll still disagree with me on this, but i've said all I feel I need to on this subject.
What determines what is included in balance changes? Does Bioware make a list? Does that not mean they have to do empirical testing to determine what is on that list? Does that not defeat the whole objective here? Are players voting a hundreds of sub-polls to decide the options of the official poll? What happens when people only want to buff everything and get super-power creeps. An inevitable response would be "well the community will nerf it back down when thing get too powerful", but what makes you think that? What happens when rather than logical nerfs to overpowered abilities, the community instead tries to buff everything else to compete with the OP things? When everything keeps getting stronger and stronger, what happens to the game's difficulty? When everyone can blast through a platinum game with a team of scimitars, what keeps them interested in the game? One might reply to that with that "people won't make the game easy-mode because they enjoy playing the game and being challenged more than winning", to which I would reply a big fat lol, probably with an accompanied gif. People farm all the time, because what they want is credits. Why wouldn't most people want to blow through an easy game with OP weapons to get tons of credits to buy more OP weapons?
I had another thing I wanted to say, but I seem to have forgotten it...Maybe i'll remember later.
Anyway, most of your idea is based on faith in the community. Faith which frankly it doesn't deserve. There may be a few examples of forumites with good ideas, but within the community as a whole, you could count them on your fingers.
TL;DR: If you didn't have the patience to read it, you don't really care what i'm saying.