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Your system would look like capitalism, but it would be much worse. Because this "big state" would be a giant company whose income does not come from free trade, but taxation. This should be a nightmare to everyone.
States generally make money only through taxation, with the exception of some nationalized industries.
You won't be able to share your BIR. Of course, you will be able to give the money to someone if you want to. Why you'd do that without something worthwhile in exchange is beyond me. I don't see how you'd end up with people getting other people's money outside of criminal coercion, which can be defended by the courts.
Don't you find this idea a bit repulsing? Can't you see it basically consist in treating humans as cattle?
I know there's a lot of opposition to the idea of identifying yourself, and personally I can't understand it. Even now you willingly take a nickname on this forums to identify yourself, therefore branding your online persona in some way. Would it be better if we let you choose the code that would be on your eartag?

I'm joking, of course, but a public database holding your fingerprints and your name on record is hardly a large breach of privacy. And I guess if you want to opt out, then you should be able to, but no state support would be given then.
But no, you want your share of the cake, without putting any fucking effort about it, not even spending a penny. Seriously, this is despicable.
Now, stocks and shares are quite an interesting animal. First of all, to buy them, you have to have some capital. Money makes more money. If you don't have the starting capital and your living expenses keep eating up your minimum-wage job earnings, you'll never make it to the stockmarket. And not for lack of trying.
Second, I believe an argument can be made that relying on income from stocks is an unproductive life. You are not helping the community in an way, you are not producing something, your are not providing a service. The only thing you are doing is moving money from one place to another, and making more money in the process. A counter-argument is that you provide starter capital for companies that could better society if given a chance... but do you? Or do you just buy low, sell high with random stocks, or even worse, survive on dividents from the already established companies?
Some things to think about
