Not yet, but probably in the next 1 - 2 years. Any website that any proposes for this purpose is not trustworthy unfortunately.
I would not guarantee it will be any different then now, except that you can pay in bitcoin.
The websites you purchase from still will be under same laws, so it is no easier to buy the stocks like OP mentioned. They still have to do KNC stuff. It will never be straight BTC to stock without a broker. You have to know who is buying to prevent fraud, insider trading, etc.