Why isn't that possible?! At least I haven't seen the possibility anywhere. It's a huge gap in the market! I'd even buy stocks with 5% or more fees and pay with Bitcoin.
Because no such project has been done yet. Moreover since crypto are not completely legalized we might not see something like that soon. However if @o_e_l_e_o is correct then you should check those sites out and see if they suit you. May vary depending on which country you are in and depending on what stock you actually want to buy since it will be listed on separate exchanges
Point is that you are not the first person to think of this, I am sure someone has thought the same and hit a wall trying to develop a project in similar objectives. Quite possibly the failed in my assumption.
But you can sell your bitcoins for fiat and use that to pay your broker. But it is thus the long route and not the streamlined one.