Actually this is already happening so you don't have to wait for that long term. All we have to wait i guess is the more and more country will adopt this kind of technology.
It has to be a Asian country for me to adopt this, though again it may take long or it may never happen as you all say. Usa has already ruled against Bitcoin so no chance seeing this happening there, but future is full of surprises Wait and watchn
Can I ask what company offers the service to buy stocks with bitcoins?
I just made a little google search, and the first thing that came up was bitbulls.
But honestly, I have read the FAQs and it sounds a little fishy to me. They don't retain transaction historys, require no ID documents or even personal data.
I don't think at this time legally any company does. This was a question for the future, currently as far I know it's is not legal to do this. The one you are referring has to be a scam, why else would they not require documentation and all.