This is entirely feasible, the only problem is that the government does not accept it. Basically, Bitcoin has not yet been accepted as an official currency like fiat, its value is still very vague. Therefore, using bitcoin directly to buy stocks is impossible, you can only through intermediary transactions with cash to buy stocks. And on the other hand, the stock can't be put on the blockchain either,
Well bitcoin and other cryptocurrencies will not be welcomed by the government as long as it contains high volatility which is absolutely impossible to become. Stock market and Crypto market is a well separated market by the means of trading on which the government has favored the stock market coz they are earning from it.
the stock represents part of a conglomerate's control, which means the controller has to be identified publicly, but for bitcoin, it seems to have can hide their identity.
Yeah, that is the main reason why government do not want to take risk with bitcoin because of money laundering by which it can be easily pull off with bitcoin.